Kyushu University Academic Staff Educational and Research Activities Database
List of Papers
Kaname Matsue Last modified date:2021.10.07

Associate Professor / Division of Applied Mathematics / Institute of Mathematics for Industry

1. Yu Ichida, Kaname Matsue and Takashi Okuda Sakamoto, A refined asymptotic behavior of traveling wave solutions for degenerate nonlinear parabolic equations, JSIAM Letters, 1-4, 2020.10, In this paper, we consider the asymptotic behavior of traveling wave solutions of the degenerate nonlinear parabolic equation: $u_{t}=u^{p}(u_{xx}+u)-¥delta u¥, (¥delta = 0 or 1)$ for $¥xi ¥equiv x - ct ¥to - ¥infty$ with $c>0$.
We give a refined one of them, which was not obtain in the preceding work [Ichida-Sakamoto, J. Elliptic and Parabolic Equations, to appear], by an appropriate asymptotic study and properties of the Lambert $W$ function..
2. Kaname Matsue, Akitoshi Takayasu, Numerical validation of blow-up solutions with quasi-homogeneous compactifications , Numerische Mathematik, 10.1007/s00211-020-01125-z, 50 pages, 2020.06, [URL].
3. Kaname Matsue, Akitoshi Takayasu, Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearity , Journal of Computational and Applied Mathematics, 2020.02, Our concerns here are blow-up solutions for ODEs with exponential nonlinearity from the viewpoint of dynamical systems and their numerical validations.
As an example, the finite difference discretization of $u_t = u_{xx} + e^{u^m}$ with the homogeneous Dirichlet boundary condition is considered.
Our idea is based on compactification of phase spaces and time-scale desingularization as in previous works.
In the present case, treatment of exponential nonlinearity is the main issue.
Fortunately, under a kind of exponential homogeneity of vector field, we can treat the problem in the same way as polynomial vector fields.
In particular, we can characterize and validate blow-up solutions with their blow-up times for differential equations with such exponential nonlinearity in the similar way to previous works.
A series of technical treatments of exponential nonlinearity in blow-up problems is also shown with concrete validation examples.
4. Kaname Matsue, Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs, Journal of Differential Equations, 10.1016/j.jde.2019.07.022, 267, 12, 7313-7368, 2019.12, Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the type of invariant sets at infinity via compactifications of phase spaces, and dynamics on their center-stable manifolds. In particular, we show that dynamics on center-stable manifolds of invariant sets at infinity with appropriate time-scale desingularizations as well as blowing-up of singularities characterize dynamics of blow-up solutions as well as their rigorous blow-up rates. Similarities for characterizing finite-time extinction and asymptotic behavior of compacton traveling waves to blow-up solutions are also shown..
5. Kaname Matsue, Shikhar Mohan, Moshe Matalon, Effect of gravity on hydrodynamically unstable flames, The 12th Asia-Pacific Conference on Combustion, 2019.07, The hydrodynamic instability, due to the large deviation of density between fresh cold mixture and hot combusted products, was discovered by Darrieus and Landau. After seven or eight decades, many aspects of this intrinsic flame instability have been revealed, such as the effects of the flame front curvature and of flow strain rate, its influence on turbulent flames and the self-wrinkling and self-turbulization of expanding flames. In the present study we focus on the composite effects of thermal expansion, differential diffusion, and gravity on flame dynamics, based on a fully nonlinear, hydrodynamic model obtained by a multi-scale analysis that exploits the distinct length scales associated with such problems. The simulations verify the stabilization effect of gravity on planar flames propagating downwards, known from linear stability theory, and show that in the presence of gravity the nonlinear development beyond the stability threshold leads to cusp-like structures of smaller amplitude that propagate at a reduced speed. Finally, we observe that a judicious choice of the Markstein number, controlled by mixture composition and domain size, and of the Froude number creates richer morphological flame structures than in the absence of gravity..
6. Kaname Matsue, On blow-up solutions of differential equations with Poincare-type compactifications, SIAM Journal on Applied Dynamical Systems, doi:10.1137/17M1124498, 17, 2249-2288, 2018.08, [URL].
7. Kaname Matsue, Rigorous numerics for fast-slow systems with one-dimensional slow variable: topological shadowing approach, Topological Methods in Nonlinear Analysis, doi=, 50, 2, 357-468, 2017.12.
8. Norio Konno, Kaname Matsue, Hideo Mitsuhashi and Iwao Sato, Quaternionic quantum walks of Szegedy type and zeta functions of graphs, Quantum Information & Computation, 17, 1349-1371, 2017.12.
9. Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, Quantum Search on Simplicial Complexes, Quantum Studies: Mathematics and Foundations,, 1-27, 2017.10.
10. Kaname Matsue and Kyoko Tomoeda, Toward a mathematical analysis for a model of suspension flowing down an inclined plane, Proceedings of EquaDiff 2017 Conference, 349-358, 2017.09.
11. Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, A note on the spectral mapping theorem of quantum walk models, Interdisciplinary Information Sciences, 23, 105-114, 2017.03.
12. Yasuaki Hiraoka, Takenobu Nakamura, Akihiko Hirata, Emerson G. Escolar, Kaname Matsue and Yasumasa Nishiura, Hierarchical structures of amorphous solids characterized by persistent homology, Proceedings of the Nathonal Academy of Sciences, 113, 26, 7035-7040, 2016.06.
13. Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, Quantum walks on simplicial complexes, Quantum Information Processing, 15, 5, 1865-1896, 2016.02.
14. Kaname Matsue, Hisashi Naito, Numerical studies of the optimization of the first eigenvalue of the heat diffusion in inhomogeneous media, Japan Journal of Industrial and Applied Mathematics, 32, 2, 489-512, 2015.10.
15. Akihiko Hirata, L.J. Kang, Takeshi Fujita, B. Klumov, Kaname Matsue, Motoko Kotani, A.R. Yavari and Mingwei Chen, Geometric frustration of icosahedron in metallic glasses, Science, 341, 6144, 376-379, 2013.07.
16. Kaname Matsue, Rigorous numerics for stationary solutions of dissipative PDEs - Existence and local dynamics -, NOLTA, 4, 1, 62-79, 2013.07.
17. Kaname Matsue, Rigorous verification of bifurcations of differential equations via the Conley index theory, SIAM Journal on Applied Dynamical Systems, 10, 1, 325-359, 2011.07.