Faculty Profiles - SEGATA JUNICHI

Information

写真a

SEGATA JUNICHI

Organization

Faculty of Mathematics Division of Analysis Professor
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）
Joint Graduate School of Mathematics for Innovation （Concurrent）

Contact information

Profile

I have been studying the long time behavior of solution to the nonlinear partial differential equations arising from physics and engineering via the harmonic analysis method. Especially, I am interested in so called nonlinear dispersive equations such as KdV and nonlinear Schrodinger equations and study the large time behavior of solutions to those equations from the point of view of scattering and soliton.

External link

Degree

Doctor of Philosophy (Mathematics)

Research History

平成18年4月〜平成22年9月　福岡教育大学教育学部平成22年10月〜平成31年3月東北大学大学院理学研究科

Research Interests・Research Keywords

Research theme： Long time behavior of solution to nonlinear dispersive partial differential equation

Keyword： partial differential equation, harmonic analysis

Research period： 2019.4 - 2031.3

Awards

福原賞

2016.12 日本数学会函数方程式論分科会渦糸にまつわる非線形分散型方程式の数学解析に関して
建部賢弘奨励賞

2007.9 日本数学会高階非線形分散型微分方程式の解の漸近挙動の研究に関して

Papers

On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension Reviewed International journal

Satoshi Masaki, Jun-ichi Segata, and Kota Uriya

Transactions of the American Mathematical Society, Ser. B 9 517 - 563 2022.6

　More details

Language：English Publishing type：Research paper (scientific journal)
Long range scattering for the nonlinear Schrodinger equation with higher order anisotropic dispersion in two dimensions Reviewed International journal

Jean-Claude Saut and Jun-ichi Segata

Journal of Mathematical Analysis and Applications 483 2020.3

　More details

Language：English Publishing type：Research paper (scientific journal)

This paper is concerned with long time behavior of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion (4NLS). We prove the long range scattering for (4NLS) with the quadratic nonlinearity in two dimensions. More precisely, We construct a solution to (4NLS) which converges to prescribed asymptotic profile as t tends to infinity, where asymptotic profile is given by the leading term of the solution to the linearized equation of (4NLS) with a logarithmic phase correction.
Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions Reviewed International journal

Satoshi Masaki, Jun-ichi Segata and Kota Uriya

Journal de Mathematiques Pures et Appliquees. 139 177 - 203 2020.2

　More details

Language：English Publishing type：Research paper (scientific journal)
Modified scattering for the 1d cubic NLS with a repulsive delta potential Reviewed International journal

Satoshi Masaki, Jason Murphy, Jun-ichi Segata

International Mathematics Research Notices 2019 ( 24 ) 7577 - 7603 2019.12

　More details

Language：English Publishing type：Research paper (scientific journal)

We consider the initial-value problem for the one dimensional cubic nonlinear Schr"odinger equation with a repulsive delta potential. We prove that small initial data in a weighted Sobolev space lead to global solutions that exhibit modified scattering.
Refinement of Strichartz estimate for Airy equation in non-diagonal case and its application Reviewed International journal

Satoshi Masaki, Jun-ichi Segata

SIAM Journal on Mathematical Analysis 50 ( 3 ) 2839 - 2866 2018.4

　More details

Language：English Publishing type：Research paper (scientific journal)

In this paper, we give an improvement of non-diagonal Strichartz estimates for Airy equation by using a Morrey type space.
As its applications, we prove the small data scattering and the existence of special non-scattering solutions, which are minimal in a suitable sense, to the mass-subcritical generalized Korteweg-de Vries equation. Especially, a use of the refined non-diagonal estimate removes several technical restrictions on the previous work about the existence of the special
non-scattering solution.

DOI： 10.1137/17M1153893
Existence of a minimal non-scattering solution to the mass sub-critical generalized Korteweg-de Vries equation Reviewed International journal

Satoshi Masaki, Jun-ichi Segata

Annales de l'Institut Henri Poincar'e/Analyse non lin'eaire 35 ( 2 ) 283 - 326 2018.4

　More details

Language：English Publishing type：Research paper (scientific journal)

In this article, we prove the existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical
generalized Korteweg-de Vries equation in the scale critical Fourier Lebesgue space. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to Fourier Lebesgue space-framework and approximation of solutions to the generalized KdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schr"odinger equation.

DOI： 10.1016/j.anihpc.2017.04.003
Modified scattering for the quadratic nonlinear Klein-Gordon equation in two dimensions Reviewed International journal

Satoshi Masaki, Jun-ichi Segata

Transactions of the American Mathematical Society 370 ( 11 ) 8155 - 8170 2018.4

　More details

Language：English Publishing type：Research paper (scientific journal)

In this paper, we consider the long time behavior of solution to the quadratic gauge invariant nonlinear Klein-Gordon equation in two space dimensions. For a given asymptotic profile, we construct a solution to this equation which converges to given asymptotic profile as t goes infinity. Here the asymptotic profile is given by the leading term of the solution to the linear Klein-Gordon equation with a logarithmic phase correction. Construction of a suitable approximate solution is based on Fourier series expansion of the nonlinearity.

DOI： 10.1090/tran/7262
The fourth order nonlinear Schr"odinger limit for quantum Zakharov system Reviewed International journal

Yung-Fu Fang, Chi-Kun Lin, Jun-ichi Segata

Zeitschrift f"ur angewandte Mathematik und Physik, ZAMP - Journal of Applied Mathematics and Physics 67 ( 6 ) 2016.4

　More details

Language：English Publishing type：Research paper (scientific journal)

This paper is concerned with the quantum Zakharov system. We prove that when the ionic speed of sound goes to infinity, the solution to the fourth order Schr"odinger part of the quantum Zakharov system converges to the solution to quantum modified nonlinear Schr"odinger eqaution.

DOI： 10.1007/s00033-016-0740-1
On well-posedness of generalized Korteweg-de Vries equation in scale critical hat L^r space Reviewed International journal

Satoshi Masaki, Jun-ichi Segata

Analysis & PDE 9 ( 3 ) 699 - 725 2016.4

　More details

Language：English Publishing type：Research paper (scientific journal)

The purpose of this paper is to study local and global well-posedness of initial value problem for the generalized Korteweg-de Vries equation in Fourier Lebesgue　space. We show (large data) local well-posedness, small data global well-posedness, and small data scattering for generalized KdV equation in the scale critical Fourier Lebesgue space. A key ingredient is a Stein-Tomas type inequality for the Airy equation, which generalizes usual Strichartz' estimates for Fourier Lebesgue space-framework.

DOI： 10.2140/apde.2016.9.699
Final state problem for the cubic nonlinear Schr"odinger equation with repulsive delta potential Reviewed International journal

Jun-ichi Segata

Communications in Partial Differential Equations 40 ( 2 ) 309 - 328 2015.4

　More details

Language：English Publishing type：Research paper (scientific journal)

We consider the asymptotic behavior in time of solutions to the cubic nonlinear Schr"odinger equation with repulsive delta potential. We shall prove that for a given small asymptotic profile, there exists a solution to this equation which converges to given asymptotic profile as t to infinity. To show this result we exploit the distorted Fourier transform associated to the Schr"odinger equation with delta potential.

DOI： 10.1080/03605302.2014.930753
Refined energy inequality with application to well-posedness for the fourth order nonlinear Schr"odinger type equation on torus Reviewed International journal

Jun-ichi Segata

Journal of Differential Equations 252 ( 11 ) 5994 - 6011 2012.4

　More details

Language：English Publishing type：Research paper (scientific journal)

We consider the time local and global well-posedness for the fourth order nonlinear Schr"odinger type equation on the torus. The nonlinear term contains the derivatives of unknown function and this prevents us to apply the classical energy method. To overcome this difficulty, we introduce the modified energy and derive an a priori estimate for the solution to this equation.

DOI： 10.1016/j.jde.2012.02.016
Existence and Stability of standing waves of fourth order nonlinear Schr"odinger type equation related to vortex filament Reviewed International journal

Masaya Maeda, Jun-ichi Segata

Funkcialaj Ekvacioj 54 ( 1 ) 1 - 14 2011.4

　More details

Language：English Publishing type：Research paper (scientific journal)

In this paper, we study the fourth order nonlinear Schr"odinger type equation which is a generalization of the Fukumoto-Moffatt model that arises in the context of the motion of a vortex filament. Firstly, we mention the existence of standing wave solution and the conserved quantities. We next investigate the case that the equation is completely integrable and show that the standing wave is orbitally stable in Sobolev spaces.

DOI： 10.1619/fesi.54.1
On asymptotic behavior of solutions to Korteweg-de type equations related to vortex filament with axial flow Reviewed International journal

Jun-ichi Segata

Journal of Differential Equations 245 ( 2 ) 281 - 306 2008.4

　More details

Language：English Publishing type：Research paper (scientific journal)

We study the global existence and asymptotic behavior in time of solutions to the Korteweg-de Vries type equation called as ``Hirota" equation. This equation is a mixture of cubic nonlinear Schr"odinger equation and modified Korteweg-de Vries equation. We show the unique existence of the solution for this equation which tends to the given modified free profile by using the two asymptotic formulae for some oscillatory integrals.

DOI： 10.1016/j.jde.2008.03.031
Modified wave operators for the fourth-order non-linear Schr"odinger-type equation with cubic non-linearity Reviewed International journal

Jun-ichi Segata

Mathematical Methods in the Applied Sciences 29 ( 15 ) 1785 - 1800 2006.4

　More details

Language：English Publishing type：Research paper (scientific journal)

We consider the scattering problem for the fourth order nonlinear Schr"odinger type equation. We show the existence of the modified wave operators for this equation by imposing the mean zero condition for the final data.

DOI： 10.1002/mma.751
Time local well-posedness for the Benjamin-Ono equation with large initial data Reviewed International journal

Naoyasu Kita, Jun-ichi Segata

Publications of the Research Institute for Mathematical Sciences, Kyoto University 42 ( 1 ) 143 - 171 2006.1

　More details

Language：English Publishing type：Research paper (scientific journal)

This paper studies the time local well-posedness of the solution to the Benjamin-Ono equation. Our aim is to remove smallness condition on the initial data which was imposed in Kenig-Ponce-Vega's work.

DOI： 10.2977/prims/1166642062
Remark on well-posedness for the fourth order nonlinear Schr"odinger type equation Reviewed International journal

Jun-ichi Segata

Proceedings of the American Mathematical Society 132 ( 12 ) 3559 - 3568 2004.12

　More details

Language：English Publishing type：Research paper (scientific journal)

We consider the initial value problem for the fourth order nonlinear Schr"odinger type equation related to the theory of vortex filament. In this paper we prove the time local well-posedness for this equation in the Sobolev space.

DOI： 10.1090/S0002-9939-04-07620-8
Scattering for quantum Zakharov system in two space dimensions Reviewed

Jun-ichi Segata

Proceedings of the American Mathematical Society 152 ( 8 ) 3367 - 3379 2024.8 （ ISSN:0002-9939 eISSN:1088-6826 ）

　More details

Language：English Publishing type：Research paper (scientific journal) Publisher：Proceedings of the American Mathematical Society

In this paper, we study long time behavior of solution to the quantum Zakharov system in two dimensions. We construct a small global solution to the quantum Zakharov system which scatters to a given free solution by using space-time resonance method developed by Gustafson-Nakanishi-Tsai [Commun. Contemp. Math. 11 (2009), pp. 657–707] and Germain-Masmoudi-Shatah [Int. Math. Res. Not. IMRN 3 (2009), 414–432; J. Math. Pures Appl. (9) 97 (2012), pp. 505–543] etc.

DOI： 10.1090/proc/16774

Web of Science

Scopus
Global Dynamics Below Excited Solitons for the Non-Radial NLS with Potential Reviewed International coauthorship

Satoshi Masaki, Jason Murphy, and Jun-ichi Segata

Indiana University Mathematics Journal 73 ( 3 ) 1097 - 1205 2024 （ ISSN:0022-2518 eISSN:1943-5258 ）

　More details

Language：English Publishing type：Research paper (scientific journal)

Web of Science
Asymptotic Behavior in Time of Solution to System of Cubic Nonlinear Schrödinger Equations in One Space Dimension

Masaki S., Segata J.I., Uriya K.

Springer Proceedings in Mathematics and Statistics 451 119 - 180 2024 （ ISSN:21941009 ISBN:9789819703630 ）

　More details

Publisher：Springer Proceedings in Mathematics and Statistics

In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Schrödinger equations in one space dimension. It turns out that for a system there exists a small solution of which asymptotic profile is a sum of two parts oscillating in a different way. This kind of behavior seems new. Further, several examples of systems which admit solution with several types of behavior such as modified scattering, nonlinear amplification, and nonlinear dissipation, are given. We also extend our previous classification result of nonlinear cubic systems.

DOI： 10.1007/978-981-97-0364-7_5

Scopus
Linear decay property for the hyperbolic-parabolic coupled systems of thermoviscoelasticity Reviewed International journal

Priyanjana M.N. Dharmawardane, Shuichi Kawashima, Takayoshi Ogawa, and Jun-ichi Segata

Journal of Hyperbolic Differential Equations 20 967 - 986 2023.12

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1142/S0219891623500297
Asymptotic stability of solitary waves for the 1d NLS with an attractive delta potential Reviewed International journal

Satoshi Masaki, Jason Murphy, and Jun-ichi Segata

Discrete and Continuous Dynamical Systems 43 2137 - 2185 2023.6

　More details

Language：English Publishing type：Research paper (scientific journal)
Polynomial deceleration for a system of cubic nonlinear Schrodinger equations in one space dimension Reviewed International journal

Naoyasu Kita, Satoshi Masaki, Jun-ichi Segata, and Kota Uriya

Nonlinear Analysis 230 2023.2

　More details

Language：English Publishing type：Research paper (scientific journal)
Asymptotic behavior in time of solutions to complex valued nonlinear Klein-Gordon equation in one space dimension Reviewed International journal

Jun-ichi Segata

Hokkaido Mathematical Journal 50 187 - 205 2021.8

　More details

Language：English Publishing type：Research paper (scientific journal)
Stability of small solitary waves for the 1d NLS with an attractive delta potential Reviewed International journal

Satoshi Masaki, Jason Murphy, Jun-ichi Segata

Analysis & PDE 13 ( 4 ) 1099 - 1128 2020.4

　More details

Language：English Publishing type：Research paper (scientific journal)
Asymptotic behavior in time of solution to the nonlinear Schr"odinger equation with higher order anisotropic dispersion Reviewed International journal

Jean-Claude Saut, Jun-ichi Segata

Discrete and Continuous Dynamical Systems. Series A 39 ( 1 ) 219 - 239 2019.4

　More details

Language：English Publishing type：Research paper (scientific journal)

We consider the asymptotic behavior in time of solutions to the nonlinear Schr"odinger equation with fourth order anisotropic dispersion which describes the propagation of ultrashort laser pulses in a medium with anomalous time dispersion in the presence of fourth-order time-dispersion. We prove existence of a solution to this equation which scatters to a solution of the linearized equation.

DOI： 10.3934/dcds.2019009
Modified scattering for the Klein-Gordon equation with the critical nonlinearity Invited Reviewed International journal

Satoshi Masaki, Jun-ichi Segata

Communications on Pure and Applied Analysis 17 ( 4 ) 1595 - 1611 2018.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.3934/cpaa.2018076
On the standing waves of quantum Zakharov system Reviewed International journal

Yung-Fu Fang, Jun-ichi Segata, Tsung-Fang Wu

Journal of Mathematical Analysis and Applications 458 ( 2 ) 1427 - 1448 2018.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1016/j.jmaa.2017.10.033
Propagation of regularity and persistence of decay for fifth order dispersive models Reviewed International journal

Jun-ichi Segata, Derek L. Smith

Journal of Dynamics and Differential Equations 29 ( 2 ) 701 - 736 2017.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1007/s10884-015-9499-x
The generalized Korteweg-de Vries equation with time oscillating nonlinearity in scale critical Sobolev space Reviewed International journal

Jun-ichi Segata, Keishu Watanabe

Nonlinear Differential Equations and Applications, NoDEA 23 ( 5 ) 2016.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1007/s00030-016-0405-y
Initial value problem for the fourth order nonlinear Schr"odinger type equation on torus and orbital stability of standing waves Reviewed International journal

Jun-ichi Segata

Communications on Pure and Applied Analysis 14 ( 3 ) 843 - 859 2015.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.3934/cpaa.2015.14.843
Long time behavior of solutions to non-linear Schr"odinger equations with higher order dispersion Invited Reviewed International journal

Jun-ichi Segata

Advanced Studies in Pure Mathematics 64 151 - 162 2015.4

　More details

Language：English Publishing type：Research paper (international conference proceedings)
WKB analysis of the Schr"odinger-KdV system Reviewed International journal

Chi-Kun Lin, Jun-ichi Segata

Journal of Differential Equations 256 ( 11 ) 3817 - 3834 2014.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1016/j.jde.2014.03.001
Orbital stability of two parameter family of solitary waves for fourth order nonlinear Schr"odinger type equation Reviewed International journal

Jun-ichi Segata

Journal of Mathematical Physics 54 ( 6 ) 2013.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1063/1.4811522
The initial value problem for some hyperbolic-dispersive system Reviewed International journal

Shuichi Kawashima, Chi-Kun Lin, Jun-ichi Segata

Mathematical Methods in Applied Sciences 35 ( 2 ) 125 - 133 2011.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1002/mma.1542
Well-posedness and standing waves for the fourth-order non-linear Schr"odinger-type equation Invited Reviewed International journal

Jun-ichi Segata

RIMS Kokyuroku Bessatsu B26 81 - 92 2011.4

　More details

Language：English Publishing type：Research paper (international conference proceedings)
A remark on asymptotics of solutions to Schr"odinger equation with fourth order dispersion Reviewed International journal

Jun-ichi Segata

Asymptotic Analysis 75 ( 1-2 ) 25 - 36 2011.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.3233/ASY-2011-1051
Well-posedness and existence of standing waves for the fourth order nonlinear Schr"odinger type equation Reviewed International journal

Jun-ichi Segata

Discrete and Continuous Dynamical Systems 27 ( 3 ) 1093 - 1105 2010.4

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.3934/dcds.2010.27.1093
Final state problem for some KdV type equation Invited Reviewed International journal

Jun-ichi Segata

RIMS Kokyuroku Bessatsu B22 13 - 20 2010.4

　More details

Language：English Publishing type：Research paper (international conference proceedings)
Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schr"odinger type equation Reviewed International journal

Jun-ichi Segata, Akihiro Shimomura

Communications in Applied Analysis 11 ( 2 ) 169 - 188 2007.4

　More details

Language：English Publishing type：Research paper (scientific journal)
On asymptotic behavior of solutions to the fourth order cubic nonlinear Schr"odinger type equation Reviewed International journal

Jun-ichi Segata

Advanced Studies in Pure Mathematics 47 329 - 339 2007.4

　More details

Language：English Publishing type：Research paper (international conference proceedings)
Asymptotics of solutions to the fourth order Schr"odinger type equation with a dissipative nonlinearity Reviewed International journal

Jun-ichi Segata, Akihiro Shimomura

Journal of Mathematics of Kyoto University 46 ( 2 ) 439 - 456 2006.4

　More details

Language：English Publishing type：Research paper (scientific journal)
The contraction mapping approach for the Benjamin-Ono equation with large initial data Reviewed International journal

Naoyasu Kita, Jun-ichi Segata

``Nonlinear Dispersive Equations" Edited by T. Ozawa and Y. Tsutsumi, GAKUTO International Series, Mathematical Sciences and Applications 26 129 - 140 2006.4

　More details

Language：English Publishing type：Research paper (international conference proceedings)
Well-posedness for the Boussinesq-type system related to the water wave Reviewed International journal

Naoyasu Kita, Jun-ichi Segata

Funkcialaj Ekvacioj 47 ( 2 ) 329 - 350 2004.8

　More details

Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1619/fesi.47.329
Well-posedness for the fourth-order nonlinear Schr"odinger-type equation related to the vortex filament Reviewed International journal

Jun-ichi Segata

Differential and Integral Equations 16 ( 7 ) 841 - 864 2003.7

　More details

Language：English Publishing type：Research paper (scientific journal)

▼display all

Presentations

デルタポテンシャルをもつ非線形シュレディンガー方程式の解の長時間挙動 Invited

瀬片純市

日本数学会2020年度秋季総合分科会 2020.9

　More details

Event date： 2021.9

Language：Japanese Presentation type：Oral presentation (invited, special)

Venue：オンライン開催 Country：Japan

本講演では、デルタポテンシャルをもつ非線形シュレディンガー方程式の解の長時間挙動について、眞崎聡氏(大阪大)、Jason Murphy氏(ミズーリ工科大)との共同研究により得られた成果(散乱問題及びソリトンの漸近安定性)について紹介した。
Modified scattering for the complex valued nonlinear Klein-Gordon equation Invited International conference

Jun-ichi Segata

Colloquia at Department of Mathematics and Statistics, Missouri University of Science and Technology 2019.12

　More details

Event date： 2019.12

Language：English Presentation type：Oral presentation (general)

Venue：Missouri University of Science and Technology Country：United States
Modified scattering for the Klein-Gordon equation with the critical nonlinearity in two and three dimensions Invited International conference

Jun-ichi Segata

RIMS 研究集会, Nonlinear Wave and Dispersive Equations 2017.8

　More details

Event date： 2019.4

Language：English Presentation type：Oral presentation (general)

Venue：京都大学数理解析研究所 (京都市) Country：Japan
Refinement of Strichartz estimates for Airy equation and application Invited International conference

Jun-ichi Segata

RIMS研究集会, 保存則と保存則をもつ偏微分方程式に対する解の正則性,特異性および長時間挙動の研究 2016.6

　More details

Event date： 2019.4

Language：English Presentation type：Oral presentation (general)

Venue：京都大学数理解析研究所 (京都市) Country：Japan
Scattering problem for the generalized Korteweg‐de Vries equation Invited International conference

Jun-ichi Segata

2016 Taiwan-Japan Workshop on Dispersion, Navier Stokes, Kinetic, and Inverse Problems 2016.12

　More details

Event date： 2019.4

Language：English Presentation type：Oral presentation (general)

Venue：National Cheng Kung University (Tainan) Country：Taiwan, Province of China
Scattering problem for the generalized Korteweg-de Vries equation Invited International conference

Jun-ichi Segata

PDE/Applied seminar at UCSB 2017.3

　More details

Event date： 2019.4

Language：English Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：University of California, Santa Barbara (Santa Barbara) Country：United States
Existence of a minimal non-scattering solutions to the mass-subcritical generalized Korteweg-de Vries equation Invited International conference

Jun-ichi Segata

RIMS研究集会, 偏微分方程式の解の形状解析 2017.6

　More details

Event date： 2019.4

Language：English Presentation type：Oral presentation (general)

Venue：京都大学数理解析研究所 (京都市) Country：Japan
Modified scattering for the 1d cubic NLS with a repulsive delta potential Invited International conference

Jun-ichi Segata

The 12th bi-annual Conference on Dynamical Systems, Differential Equations and Applications 2018.7

　More details

Event date： 2018.7

Language：English Presentation type：Oral presentation (general)

Venue：National Taiwan University (Taipei) Country：Taiwan, Province of China

We consider the initial value problem for the cubic nonlinear Schr"odinger equation (NLS) with a repulsive delta potential in one space dimension. Our goal is to describe the long-time decay and asymptotics of small solutions to (NLS). From the linear scattering theory, we expect that (NLS) will not scatter to the solution to the linear equation. We prove that if the initial data is sufficiently small in a weighted Sobolev space, then there exists a unique global solution to (NLS) that exhibits modified scattering.
Refinement of Strichartz estimates for Airy equation in non-diagonal case and application Invited International conference

Jun-ichi Segata

RIMS workshop Harmonic Analysis and Nonlinear Partial Differential Equations 2018.6

　More details

Event date： 2018.6

Language：English Presentation type：Oral presentation (general)

Venue：京都大学数理解析研究所 (京都市) Country：Japan
Modified scattering for the 1d cubic NLS with a repulsive delta potential Invited International conference

Jun-ichi Segata

Taiwan-Japan Workshop on Dispersion and Nonlinear Waves 2018.6

　More details

Event date： 2018.6

Language：English Presentation type：Oral presentation (general)

Venue：National Cheng Kung University (Tainan) Country：Taiwan, Province of China
Modified scattering for the Klein-Gordon equation with critical nonlinearity in two and three dimensions Invited International conference

Jun-ichi Segata

Nonlinear PDE for Future Applications - Hyperbolic and Dispersive PDE - 2017.7

　More details

Event date： 2017.7 - 2019.4

Language：English Presentation type：Oral presentation (general)

Venue：東北大学 (仙台市) Country：Japan
Scattering problem for the generalized Korteweg-de Vries equation Invited International conference

Jun-ichi Segata

Colloquium at Fudan University 2016.12

　More details

Event date： 2016.12

Language：English Presentation type：Oral presentation (invited, special)

Venue：Fudan University (Shanghai) Country：China
Well-posedness for the fourth order nonlinear Schr"odinger type equation and orbital stability of standing waves Invited International conference

Jun-ichi Segata

Math Colloquium at National Cheng Kung University 2015.6

　More details

Event date： 2015.6

Language：English Presentation type：Oral presentation (general)

Venue：National Cheng Kung University (Tainan) Country：Taiwan, Province of China
The higher order nonlinear dispersive equation related to the motion of vortex filament Invited International conference

Jun-ichi Segata

PDE/Applied seminar at UCSB 2014.4

　More details

Event date： 2014.4

Language：English Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：University of California, Santa Barbara (Santa Barbara) Country：United States
非線形シュレディンガー方程式系の解の長時間挙動について Invited

瀬片純市

神楽坂解析セミナー 2023.8

　More details

Event date： 2023.8

Language：Japanese Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：東京理科大学 (東京都) Country：Japan
非線形分散型方程式系の長距離散乱について Invited

瀬片純市

大阪大学数学教室談話会 2023.6

　More details

Event date： 2023.6

Language：Japanese Presentation type：Oral presentation (general)

Venue：大阪大学 (豊中市) Country：Japan
非線形シュレディンガー方程式系の解の長時間挙動について Invited

瀬片純市

大阪大学微分方程式セミナー 2023.6

　More details

Event date： 2023.6

Language：Japanese Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：大阪大学 (豊中市) Country：Japan
Asymptotic behavior in time of solution to system of cubic nonlinear Schrodinger equations in one space dimension Invited International conference

Jun-ichi Segata

RIMS研究集会 Workshop on Variational Methods and Dispersive Equations 2023.2

　More details

Event date： 2023.2

Language：English Presentation type：Oral presentation (general)

Venue：京都大学数理解析研究所 Country：Japan
非線形シュレディンガー方程式のシステムの解の長時間挙動について Invited

瀬片純市

第11回室蘭非線形解析研究会 2022.1

　More details

Event date： 2022.1

Language：Japanese Presentation type：Oral presentation (general)

Venue：オンライン講演 Country：Japan
デルタポテンシャルをもつ非線形シュレディンガー方程式の解の長時間挙動 Invited

瀬片純市

京都大学大学院理学研究科数学教室談話会 2021.6

　More details

Event date： 2021.6

Language：Japanese Presentation type：Oral presentation (general)

Venue：オンライン講演 Country：Japan
On 1d nonlinear Schrodinger equation with an attractive delta potential Invited

Jun-ichi Segata

反応拡散拡散方程式と非線形分散型方程式の解の挙動 2020.2

　More details

Event date： 2020.2

Language：Japanese Presentation type：Oral presentation (general)

Country：Japan
Asymptotic behavior in time of solution to the nonlinear Schrodinger equation with higher order anisotropic dispersion Invited

Jun-ichi Segata

Critical exponent and nonlinear evolution equations 2020 2020.2

　More details

Event date： 2020.2

Language：Japanese Presentation type：Oral presentation (general)

Venue：東京理科大学 Country：Japan
On 1d nonlinear Schrodinger equation with an attractive delta potential

Jun-ichi Segata

北九州地区における偏微分方程式研究集会 2020.2

　More details

Event date： 2020.2

Language：Japanese Presentation type：Oral presentation (general)

Venue：北九州市 Country：Japan
Modified scattering for the complex valued nonlinear Klein-Gordon equation Invited

Jun-ichi Segata

Workshop on nonlinear wave equations and related topics in Kobe 2019.11

　More details

Event date： 2019.11

Language：Japanese Presentation type：Oral presentation (general)

Venue：神戸大学 Country：Japan
Modified scattering for the complex valued nonlinear Klein-Gordon equation Invited International conference

Jun-ichi Segata

Fundamental Problems in Mathematical and Theoretical Physics 2019.7

　More details

Event date： 2019.7

Language：English Presentation type：Oral presentation (general)

Venue：早稲田大学理工学部 Country：Japan
Asymptotic behavior in time of solutions to complex valued nonlinear Klein-Gordon equation Invited

Jun-ichi Segata

京都大学NLPDEセミナー 2019.6

　More details

Event date： 2019.6

Language：Japanese Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：京都大学 Country：Japan
Asymptotic behavior in time of solutions to complex valued nonlinear Klein-Gordon equation Invited

Jun-ichi Segata

大阪大学微分方程式セミナー 2019.5

　More details

Event date： 2019.5

Language：Japanese Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：大阪大学 Country：Japan
Asymptotic behavior in time of solutions to complex valued nonlinear Klein-Gordon equation Invited

Jun-ichi Segata

九州関数方程式セミナー 2019.4

　More details

Event date： 2019.4

Language：Japanese Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：福岡大学セミナーハウス Country：Japan
Asymptotic behavior in time of solutions to complex valued nonlinear Klein-Gordon equation Invited International conference

Jun-ichi Segata

第144回熊本大学応用解析セミナー 2019.3

　More details

Event date： 2019.3

Language：English Presentation type：Oral presentation (general)

Venue：熊本大学 (熊本市) Country：Japan
On nonlinear Schr"odinger equation with attractive delta potential in one space dimension Invited

Jun-ichi Segata

Nonlinear Dispersive Equations in Kumamoto 2019.1

　More details

Event date： 2019.1

Language：Japanese Presentation type：Oral presentation (general)

Venue：熊本大学 (熊本市) Country：Japan
On 1d nonlinear Schr"odinger equation with delta potential Invited International conference

Jun-ichi Segata

シュレーディンガー方程式の数理とその周辺 2019.1

　More details

Event date： 2019.1

Language：English Presentation type：Oral presentation (general)

Venue：伊豆市立土肥公民館 (伊豆市) Country：Japan
On 1d nonlinear Schr"odinger equation with an attractive delta potential Invited

Jun-ichi Segata

九州関数方程式セミナー 2018.10

　More details

Event date： 2018.10

Language：Japanese Presentation type：Oral presentation (general)

Venue：福岡大学セミナーハウス (福岡市) Country：Japan
Modified scattering for the cubic nonlinear Schr"odinger equation with a repulsive delta potential in one space dimension Invited

Jun-ichi Segata

広島微分方程式研究会 2018.10

　More details

Event date： 2018.10

Language：Japanese Presentation type：Oral presentation (general)

Venue：広島大学 (東広島市) Country：Japan
Modified scattering for the cubic nonlinear Schr"odinger equation with a repulsive delta potential in one space dimension Invited

Jun-ichi Segata

応用解析研究会 2018.6

　More details

Event date： 2018.6

Language：Japanese Presentation type：Oral presentation (general)

Venue：早稲田大学 (東京都) Country：Japan
Refinement of Strichartz estimates for Airy equation in non-diagonal case and application Invited

Jun-ichi Segata

RIMS共同研究非線形波動及び分散型方程式の研究 2018.5

　More details

Event date： 2018.5

Language：Japanese Presentation type：Oral presentation (general)

Venue：京都大学数理解析研究所 (京都市) Country：Japan
Refinement of Strichartz estimate for Airy equation in non-diagonal case and its application Invited International conference

Jun-ichi Segata

Critical Exponents and Nonlinear Evolution Equation 2017 2017.2

　More details

Event date： 2017.2

Language：English Presentation type：Oral presentation (general)

Venue：東京理科大学 (東京都) Country：Japan
Scattering problem for the generalized Korteweg-de Vries equation Invited International conference

Jun-ichi Segata

第34回九州における偏微分方程式研究集会 2017.1

　More details

Event date： 2017.1 - 2017.2

Language：English Presentation type：Oral presentation (general)

Venue：九州大学西新プラザ (福岡市) Country：Japan
一般化Korteweg-de Vries方程式の散乱問題 Invited

Jun-ichi Segata

東北大学数学教室談話会 2017.1

　More details

Event date： 2017.1

Language：Japanese Presentation type：Oral presentation (general)

Venue：東北大学 (仙台市) Country：Japan
Final state problem for the Klein-Gordon equation with quadratic gauge invariant nonlinearity in two dimensions Invited

Jun-ichi Segata

京都大学NLPDEセミナー 2016.12

　More details

Event date： 2016.12

Language：Japanese Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：京都大学 (京都市) Country：Japan
Modified scattering for the Klein-Gordon equation with quadratic gauge invariant nonlinearity in two dimensions Invited

Jun-ichi Segata

第３回神楽坂非線形波動研究会 2016.12

　More details

Event date： 2016.12

Language：Japanese Presentation type：Oral presentation (general)

Venue：東京理科大学 (東京都) Country：Japan
Refinement of Strichartz estimates for Airy equation and application Invited International conference

Jun-ichi Segata

Nonlinear Wave and Dispersive Equations, Kyoto 2016 2016.9

　More details

Event date： 2016.9

Language：English Presentation type：Oral presentation (general)

Venue：京都大学理学部 (京都市) Country：Japan
Refinement of Strichartz estimates for Airy equation and application Invited International conference

Jun-ichi Segata

Fundamental Problems in Mathematical and Theoretical Physics 2016.7

　More details

Event date： 2016.7

Language：English Presentation type：Oral presentation (general)

Venue：早稲田大学理工学部 (東京都) Country：Japan

▼display all

Professional Memberships

The Mathematical Society of Japan

Committee Memberships

日本数学会地方区代議員 Domestic

2013.3 - 2014.2

Academic Activities

実行委員 International contribution

Critical Phenomena in Nonlinear Partial Differential Equations, Harmonic Analysis, and Functional Inequalities （ Japan ） 2023.11

　More details

Type：Competition, symposium, etc.

Number of participants：200
Screening of academic papers

Role(s)： Peer review

2023

　More details

Type：Peer review

Number of peer-reviewed articles in foreign language journals：6

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：0

Proceedings of domestic conference Number of peer-reviewed papers：0
Screening of academic papers

Role(s)： Peer review

2022

　More details

Type：Peer review

Number of peer-reviewed articles in foreign language journals：10

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：0

Proceedings of domestic conference Number of peer-reviewed papers：0
数学通信

2021.3 - 2022.2

　More details

Type：Academic society, research group, etc.
Screening of academic papers

Role(s)： Peer review

2021

　More details

Type：Peer review

Number of peer-reviewed articles in foreign language journals：7

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：0

Proceedings of domestic conference Number of peer-reviewed papers：0
Screening of academic papers

Role(s)： Peer review

2020

　More details

Type：Peer review

Number of peer-reviewed articles in foreign language journals：9

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：1

Proceedings of domestic conference Number of peer-reviewed papers：0
Kyushu Journal of Mathematics International contribution

2019.4 - Present

　More details

Type：Academic society, research group, etc.
Screening of academic papers

Role(s)： Peer review

2019

　More details

Type：Peer review

Number of peer-reviewed articles in foreign language journals：9

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：1

Proceedings of domestic conference Number of peer-reviewed papers：0
Screening of academic papers

Role(s)： Peer review

2018

　More details

Type：Peer review

Number of peer-reviewed articles in foreign language journals：3

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：0

Proceedings of domestic conference Number of peer-reviewed papers：0
Screening of academic papers

Role(s)： Peer review

2017

　More details

Type：Peer review

Number of peer-reviewed articles in foreign language journals：4

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：0

Proceedings of domestic conference Number of peer-reviewed papers：0
Screening of academic papers

Role(s)： Peer review

2016

　More details

Type：Peer review

Number of peer-reviewed articles in foreign language journals：5

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：0

Proceedings of domestic conference Number of peer-reviewed papers：0

▼display all

Research Projects

質量劣臨界非線項を持つ分散型偏微分方程式の解の大域解析

Grant number：21H00993 2021 - 2024

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

　 More details

Authorship：Principal investigator Grant type：Scientific research funding
ネットワーク上の非線形シュレディンガー方程式の解析

Grant number：21K18588 2021 - 2023

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Challenging Research(Exploratory)

　 More details

Authorship：Principal investigator Grant type：Scientific research funding
準線形双曲-放物型保存則系における時空間非一様ダイナミクスの数学解析の新展開

Grant number：20H00118 2020 - 2023

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)

　 More details

Authorship：Coinvestigator(s) Grant type：Scientific research funding
臨界型非線形数理モデルにおける高次数理解析法の創造

Grant number：19H05597 2019 - 2023

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (S)

　 More details

Authorship：Coinvestigator(s) Grant type：Scientific research funding
分散性を伴う非線形偏微分方程式の解の長時間挙動の解析

Grant number：17H02851 2017 - 2020

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

　 More details

Authorship：Principal investigator Grant type：Scientific research funding
非線形分散型方程式に対する分散波, 孤立波およびそれらの相互作用の解析

Grant number：25707004 2013 - 2016

Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (A)

　 More details

Authorship：Principal investigator Grant type：Scientific research funding
非線形分散型方程式の分散波と孤立波の相互作用の解析

2012 - 2013

住友財団基礎科学研究助成

　 More details

Authorship：Principal investigator Grant type：Contract research
非線形分散型方程式の解の長時間挙動と特異極限について

Grant number：21740122 2009 - 2012

Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

　 More details

Authorship：Principal investigator Grant type：Scientific research funding
非線形分散型方程式の解の長時間挙動について

Grant number：19840036 2007 - 2008

Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (Start-up)

　 More details

Authorship：Principal investigator Grant type：Scientific research funding
流体と水面波を記述する非線形偏微分方程式の適切性と解の挙動について

Grant number：16・06513 2004 - 2005

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows

　 More details

Authorship：Principal investigator Grant type：Scientific research funding

▼display all

Educational Activities

For education, I teach several lectures such as linear algebra, calculus and topics in analysis, and supervise a few students in their studies of mathematics.

Class subject

微分積分学Ⅱ

2023.10 - 2024.3 Second semester
非線形解析大意

2023.10 - 2024.3 Second semester
数学特論１１

2023.10 - 2024.3 Second semester
数学演習ＡⅡ

2023.10 - 2024.3 Second semester
微分積分学Ⅰ

2023.4 - 2023.9 First semester
微分積分続論Ⅰ

2023.4 - 2023.9 First semester
数学演習ＡⅠ

2023.4 - 2023.9 First semester
微分積分学Ⅱ

2022.10 - 2023.3 Second semester
数学演習ＡⅡ

2022.10 - 2023.3 Second semester
微分積分学Ⅰ

2022.4 - 2022.9 First semester
非線形解析大意

2022.4 - 2022.9 First semester
数学特論１１（非線形解析）

2022.4 - 2022.9 First semester
数学演習ＡⅠ

2022.4 - 2022.9 First semester
微分積分続論Ⅱ

2021.10 - 2022.3 Second semester
コアセミナーⅡ

2021.10 - 2022.3 Second semester
微分積分学・同演習Ⅲ

2021.4 - 2021.9 First semester
非線形解析大意

2021.4 - 2021.9 First semester
数学特論１１（非線形解析）

2021.4 - 2021.9 First semester
微分積分学・同演習Ｂ

2020.10 - 2021.3 Second semester
微分積分続論Ⅱ

2020.10 - 2021.3 Second semester
微分積分学・同演習Ａ

2020.4 - 2020.9 First semester
非線形解析大意

2020.4 - 2020.9 First semester
数学特論１１（非線形解析）

2020.4 - 2020.9 First semester
微分積分学

2019.10 - 2020.3 Second semester
複素関数論

2019.10 - 2020.3 Second semester
微分積分学・同演習B

2019.10 - 2020.3 Second semester
線形代数

2019.4 - 2019.9 First semester
微分積分学・同演習A

2019.4 - 2019.9 First semester

▼display all

FD Participation

2022.4 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2021.7 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2021.3 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]

Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

2023 大阪大学大学院理学研究科 Classification:Intensive course Domestic/International Classification:Japan

Semester, Day Time or Duration：6月
2021 京都大学大学院理学研究科 Classification:Intensive course Domestic/International Classification:Japan

Semester, Day Time or Duration：6月

Acceptance of Foreign Researchers, etc.

Department of Mathematical Sciences, Faculty of Applied Sciences, Wayamba University of Sri Lanka

Acceptance period： 2022.10 - 2023.4 （Period）：1 month or more

Nationality：Sri Lanka

Business entity：Japan Society for the Promotion of Science

Travel Abroad

2015.1 - 2015.3

Staying countory name 1：France Staying institution name 1：Universit'e de Paris-Sud, Orsay
2014.3 - 2014.10

Staying countory name 1：United States Staying institution name 1：University of California, Santa Barbara
2011.5 - 2011.9

Staying countory name 1：France Staying institution name 1：University of Cergy-Pontoise