TAKASE HIROSHI
Organization
Institute of Mathematics for Industry Division of Applied Mathematics Assistant Professor
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）
Title
Assistant Professor
Contact information
Profile
偏微分方程式の非適切問題・逆問題に関する研究を行っている．
External link
ORCID
Research Areas
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Natural Science / Mathematical analysis
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Natural Science / Applied mathematics and statistics
Degree
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Ph.D. (Mathematical Sciences)
Research History
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Kyushu University Institute of Mathematics for Industry Assistant Professor
2022.4 - Present
Education
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The University of Tokyo Graduate School of Mathematical Sciences
2017.4 - 2022.3
Research Interests・Research Keywords
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Research theme： Partial differential equations
Keyword： Partial differential equations
Research period： 2025
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Research theme： Ill-posed problems
Keyword： Ill-posed problems
Research period： 2025
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Research theme： Uniqueness of continuation
Keyword： Uniqueness of continuation
Research period： 2025
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Research theme： Geometric analysis
Keyword： Geometric analysis
Research period： 2025
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Research theme： Inverse problems
Keyword： Inverse problems
Research period： 2025
Awards
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2024.11 East Asia Section of Inverse Problems International Association Lipschitz stability for Cauchy problems of elliptic equations and applications to evolution equations
Hiroshi Takase
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研究科長賞
2022.3 東京大学大学院数理科学研究科
髙瀬裕志
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研究科長賞
2019.3 東京大学大学院数理科学研究科
Papers
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Lipschitz stability for an elliptic inverse problem with two measurements Reviewed
Mourad Choulli, Hiroshi Takase
Research in the Mathematical Sciences 12 ( 2 ) 2025.6 （ ISSN:2522-0144 eISSN:2197-9847 ）
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An inverse hyperbolic obstacle problem Reviewed
Mourad Choulli, Hiroshi Takase
Journal of Evolution Equations 25 ( 2 ) 2025.6 （ ISSN:1424-3199 eISSN:1424-3202 ）
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Global Lipschitz stability for inverse problems of wave equations on Lorentzian manifolds Reviewed
Hiroshi Takase
Journal of Differential Equations 372 564 - 590 2023.11 （ ISSN:0022-0396 eISSN:1090-2732 ）
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A Carleman estimate and an energy method for a first-order symmetric hyperbolic system Reviewed
Giuseppe Floridia, Hiroshi Takase, Masahiro Yamamoto
Inverse Problems and Imaging 16 ( 5 ) 1163 - 1178 2022.8 （ ISSN:1930-8337 eISSN:1930-8345 ）
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Inverse source problem related to one-dimensional Saint-Venant equation Reviewed
Hiroshi Takase
Applicable Analysis 101 ( 1 ) 35 - 47 2022.1 （ ISSN:00036811 ）
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Observability inequalities for degenerate transport equations Reviewed
Giuseppe Floridia, Hiroshi Takase
Journal of Evolution Equations 21 ( 4 ) 5037 - 5053 2021.12
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Inverse problems for first-order hyperbolic equations with time-dependent coefficients Reviewed
Giuseppe Floridia, Hiroshi Takase
Journal of Differential Equations 305 45 - 71 2021.12
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クローキングと波動方程式のコーシー問題の非一意性 Reviewed
髙瀬裕志
数理科学実践研究レター2021 LMSR2021 ( 7 ) 2021.8
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Infinitely many non-uniqueness examples for Cauchy problems of the two-dimensional wave and Schrödinger equations Reviewed
Hiroshi Takase
Proceedings of the Japan Academy, Series A, Mathematical Sciences 97 ( 7 ) 45 - 50 2021.7
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Inverse source problem for a system of wave equations on a Lorentzian manifold Reviewed
Hiroshi Takase
Communications in Partial Differential Equations 45 ( 10 ) 1414 - 1434 2020.10
Presentations
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Lipschitz stability for Cauchy problems of elliptic equations and applications to evolution equations Invited
Hiroshi Takase
The 8th Young Scholar Symposium, East Asia Section of Inverse Problems International Association 2024.11
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Lipschitz stability estimate for an inverse problem related to unique continuation Invited
髙瀬裕志
Workshop for young scholars Control and inverse problems on waves, oscillations and flows - Mathematical analysis and computational methods - 2024.9
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Lipschitz stability for Cauchy problems of elliptic equations Invited
Hiroshi Takase
Finland-Japan Workshop in Industrial and Applied Mathematics 2024.8
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楕円型方程式のコーシー問題に対するリプシッツ型安定性 Invited
髙瀬裕志
応用数学・数値解析に関する研究会 2024.6
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Global Lipschitz stability for inverse problems of waves on Lorentzian manifolds Invited
Hiroshi Takase
The 11th International Conference Inverse Problems: Modeling and Simulation 2024.5
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Inverse source problems for wave equations with inverse square potentials Invited
Hiroshi Takase
2024 Japan-Taiwan Joint Workshop on Numerical Analysis and Inverse Problems 2024.3
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Inverse source problems for wave equations with inverse square potentials Invited
Hiroshi Takase
2024 Japan-Taiwan Joint Workshop on Numerical Analysis and Inverse Problems 2024.3
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Inverse source problems for wave equations with inverse square potentials Invited
Hiroshi Takase
The 41th Kyushu Symposium on Partial Differential Equations 2024.1
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Inverse source problems for wave equations with inverse square potentials Invited
Hiroshi Takase
The 41th Kyushu Symposium on Partial Differential Equations 2024.1
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Lipschitz stability for inverse source problems of waves on Lorentzian manifolds
Hiroshi Takase
11th Applied Inverse Problems Conference 2023.9
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Lipschitz stability for inverse source problems of waves on Lorentzian manifolds
Hiroshi Takase
11th Applied Inverse Problems Conference 2023.9
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Unique continuation for wave equations in asymptotically anti-de Sitter spaces Invited
Hiroshi Takase
10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) 2023.8
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Unique continuation for wave equations in asymptotically anti-de Sitter spaces Invited
Hiroshi Takase
10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) 2023.8
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Inverse problems for first-order hyperbolic equations
Hiroshi Takase
The 59th ANZIAM Conference 2023.2
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Inverse problems for first-order hyperbolic equations
Hiroshi Takase
The 59th ANZIAM Conference 2023.2
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Unique continuation for wave equations in asymptotically anti-de Sitter spaces Invited
Hiroshi Takase
Workshop “Recent advances in direct and inverse problems for PDEs and applications” 2022.12
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Unique continuation for wave equations in asymptotically anti-de Sitter spaces Invited
Hiroshi Takase
Workshop “Recent advances in direct and inverse problems for PDEs and applications” 2022.12
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Unique continuation for wave equations in asymptotically anti de Sitter spaces Invited
髙瀬裕志
若手研究集会「波動・振動・流れの制御と逆問題 理論と数値計算 」 2022.11
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Unique continuation for wave equations in asymptotically anti de Sitter spaces Invited
髙瀬裕志
若手研究集会「波動・振動・流れの制御と逆問題 理論と数値計算 」 2022.11
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一階対称双曲型方程式における波源項決定逆問題 Invited
髙瀬裕志
日本応用数理学会年会 2022.9
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一階対称双曲型方程式における波源項決定逆問題 Invited
髙瀬裕志
日本応用数理学会年会 2022.9
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Inverse source problems for wave equations on Lorentzian manifolds Invited
Hiroshi Takase
10th International Conference “Inverse Problems: Modeling and Simulation” 2022.5
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Inverse source problems for wave equations on Lorentzian manifolds Invited
Hiroshi Takase
10th International Conference “Inverse Problems: Modeling and Simulation” 2022.5
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Inverse problems for wave equations with time-dependent principal parts Invited
Hiroshi Takase
RIMS Workshop on “Theory and practice in inverse problems” 2022.1
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Inverse problems for wave equations with time-dependent principal parts Invited
Hiroshi Takase
RIMS Workshop on “Theory and practice in inverse problems” 2022.1
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Observability inequalities for advection equations Invited
Hiroshi Takase
The Third Russia–Japan Workshop “Mathematical analysis of fracture phenomena for elastic structures and its applications”
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Inverse problems for first-order hyperbolic equations
髙瀬裕志
日本数学会年会
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Inverse problems through Carleman estimates for first-order hyperbolic equations Invited
Hiroshi Takase
Workshop for young scholars “Control and inverse problems on waves, oscillations and flows”
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Inverse problems for first-order hyperbolic equations Invited
Hiroshi Takase
Analysis and Numerics of Design, Control and Inverse Problems
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Inverse source problem for a system of wave equations on Lorentzian manifolds
髙瀬裕志
日本数学会年会
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Inverse problems for general first-order hyperbolic equations Invited
Hiroshi Takase
The Second Russia– Japan Workshop “Mathematical analysis of fracture phenomena for elastic structures and its applications”
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Inverse source problem for Klein–Gordon equation in de Sitter space-time
Hiroshi Takase
RIMS Workshop on “Analysis of inverse problems through partial differential equations and related topics”
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Uniqueness and stability for inverse hyperbolic problems by an internal observation
Hiroshi Takase
Russia–Japan Workshop “Mathematical analysis of fracture phenomena for elastic structures and its applications”
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双曲型逆問題における内部境界観測に対する大域リプシッツ安定性
髙瀬裕志
第41回発展方程式若手セミナー
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Global Lipschitz stability by an internal subboundary observation for inverse hyperbolic problems
Hiroshi Takase
INdAM intensive trimester “Shape optimization, control and inverse problems for PDEs”
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Inverse source problem for the gravitational waves in general relativity
Hiroshi Takase
Taiwan– Japan Joint Workshop on Inverse Problems and Related Topics
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Inverse source problem for the gravitational waves
Hiroshi Takase
Inverse problems for partial differential equations and related areas
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Inverse source problem related to the gravitational waves in general relativity
Hiroshi Takase
Analysis, Control and Inverse Problems for PDEs
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Inverse source problem related to the gravitational waves in general relativity
Hiroshi Takase
International Conference on Inverse Problems
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重力波源決定逆問題
髙瀬裕志
第40回発展方程式若手セミナー
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Inverse source problem of gravitational wave in general relativity
Hiroshi Takase
Workshop for young scholars “Control and inverse problems on waves, oscillations and flows”
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Inverse source problem related to the gravitational wave in general relativity
Hiroshi Takase
The 9th International Conference on Inverse Problems and Related Topics
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Inverse problem related to the St. Venant equation for one dimensional water flow
Hiroshi Takase
The 3rd Winter School on Computational Science and Machine Learning
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Inverse problem related to the St. Venant equation for one dimensional water flow
Hiroshi Takase
A3 Workshop on Applied Inverse Problems and Related Topics
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Inverse problem related to the St. Venant equation for one dimensional water flow
Hiroshi Takase
Taiwan–Japan Joint Workshop on Inverse Problems
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Inverse problem related to the St. Venant equation for one dimensional water flow
Hiroshi Takase
A3 Workshop on Applied Inverse Problems in 2017 CSIAM Annual Meeting
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Inverse problems for wave equations on Lorentzian manifolds Invited
髙瀬裕志
愛媛大学解析セミ ナー 2020.12
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Inverse source problems for wave equations on Lorentzian manifolds Invited
髙瀬裕志
現象数理セミナー 2022.7
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Inverse source problems for symmetric hyperbolic systems of first-order Invited
髙瀬裕志
九州関数方程式セミナー 2022.6
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漸近的アンチドジッター空間における波動方程式の一意接続性 Invited
髙瀬裕志
九大幾何学セミナー 2023.4
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Global Lipschitz stability for inverse source problems of Lorentzian wave equations Invited
Hiroshi Takase
Joint Fudan - RICAM Seminar on Inverse Problems 2023.11
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漸近的アンチドジッター空間における波動方程式の一意接続性 Invited
髙瀬裕志
九大幾何学セミナー 2023.4
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Inverse source problems for wave equations on Lorentzian manifolds Invited
髙瀬裕志
現象数理セミナー 2022.7
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Inverse source problems for symmetric hyperbolic systems of first-order Invited
髙瀬裕志
九州関数方程式セミナー 2022.6
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Global Lipschitz stability for inverse source problems of Lorentzian wave equations Invited
Hiroshi Takase
Joint Fudan - RICAM Seminar on Inverse Problems 2023.11
Professional Memberships
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Inverse Problems International Association
2022.11 - Present
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日本数学会
2021.4 - Present
Research Projects
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Grant number：25K17280 2025.4 - 2028.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists
高瀬 裕志
Grant type：Scientific research funding
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Inverse problem theory for innovation of detection methods
Grant number：23KK0049 2023.9 - 2028.3
Grants-in-Aid for Scientific Research Fund for the Promotion of Joint International Research (International Collaborative Research)
伊藤 弘道, 山本 昌宏, 奈良 高明, 劉 逸侃, 高瀬 裕志
Grant type：Scientific research funding
本研究では、検知技術の革新のための逆問題理論を構築し、理論的再構成法に裏打ちされた数値解析手法を開発することで、非破壊検査や医療画像や環境問題のような現実の問題へと応用する。具体的には、inverse source problemやinverse obstacle problemに関する以下の３つの研究課題に取り組む。
研究課題A：弾性構造物の欠陥の検出
研究課題B：汚染物質の発生源（移動する場合も含む）の位置の検出
研究課題C：人体内部の電気・機械特性異常部位の検出
課題解決のために、研究代表者を中心とする日本側研究者がフランスとオーストリアの３つの海外研究機関に滞在し、共同研究を行う。 -
Inverse problems for degenerate hyperbolic partial differential equations on manifolds
Grant number：22K20340 2022.8 - 2024.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity Start-up
Takase Hiroshi
Grant type：Scientific research funding
He studied an inverse problem for a system of hyperbolic partial differential equations written in terms of the Laplace-Beltrami operator on a Lorentzian manifold. He established a weighted energy estimate, the Carleman estimate, for this system and proved a global Lipschitz stability when the observation data is taken on a part of the boundary of the Lorentzian manifold. Furthermore, he proved a global Lipschitz stability for an inverse source problem of determining the source term of a one-dimensional wave equation with an inverse square potential.
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Inverse problems for hyperbolic partial differential equations on Lorentzian manifolds
Grant number：20J11497 2020.4 - 2022.3
Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows
Takase Giroshi
Grant type：Scientific research funding
時間依存する係数をもつ双曲型偏微分方程式について，波源項や方程式の係数を決定する逆問題，及び解の局所的な一意性を保証する一意接続性定理に関して完全な解決が待たれている．そこで本研究では曲がった時空間を記述するローレンツ多様体上での波動方程式に対し微分幾何学を取り入れた解析手法を用いることで，これらの課題に対し統一的なアプローチを用い一意性及び安定性を証明する．
Educational Activities
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解析学に関する教育に携わっている．
Class subject
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解析学Ⅱ・演習
2024.10 - 2025.3 Second semester
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フーリエ・ラプラス変換と偏微分方程式
2023.10 - 2024.3 Second semester
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解析学Ⅱ・演習
2023.10 - 2024.3 Second semester
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解析学Ⅱ・演習
2022.10 - 2023.3 Second semester
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フーリエ・ラプラス変換と偏微分方程式
2022.10 - 2023.3 Second semester
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フーリエ・ラプラス変換と偏微分方程式
2024.10 - 2025.3 Second semester