Organization
Faculty of Environmental, Life, Natural Science and Technology Lecturer
Position
Lecturer
External link
Takase Hiroshi
Degree
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Ph.D. (Mathematical Sciences) ( 2022.3 The University of Tokyo )
Research Interests
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Partial differential equations
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Uniqueness of continuation
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Geometric analysis
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Ill-posed problems
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Inverse problems
Education
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The University of Tokyo 大学院数理科学研究科
2017.4 - 2022.3
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Kyoto University 理学部
2013.4 - 2017.3
Research History
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Okayama University Department of Mathematics Lecturer
2026.4
Country：Japan
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Kyushu University Institute of Mathematics for Industry Assistant Professor
2022.4 - 2026.3
Country：Japan
Professional Memberships
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Inverse Problems International Association
2022.11
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日本数学会
2021.4
Papers
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Stability for an inverse flux and an inverse boundary coefficient problems Reviewed International coauthorship International journal
Mourad Choulli, Shuai Lu, Hiroshi Takase
Inverse Problems and Imaging 23 152 - 162 2026.8
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Local Hölder stabilities for inverse problems of first-order hyperbolic equations Reviewed International coauthorship International journal
Giuseppe Floridia, Hiroshi Takase
Analysis and Numerics of Design, Control and Inverse Problems. INDAM 2021. Springer INdAM Series 63 143 - 157 2025.10
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An inverse hyperbolic obstacle problem Reviewed
Mourad Choulli, Hiroshi Takase
Journal of Evolution Equations 25 ( 2 ) 2025.6
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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
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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
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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
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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
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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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Quantitative unique continuation for elliptic equations Invited
髙瀬 裕志
談話会 2026.6.10 岡山大学理学部数学科
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Stability for boundary determination in elliptic inverse problems and extensions to evolution equations Invited International conference
Hiroshi Takase
The 12th International Conference "Inverse Problems: Modeling and Simulation" 2026.6.1
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Stability in elliptic inverse problems for determining boundary functions Invited
Hiroshi Takase
2026 Taiwan-Japan Joint Workshop on Inverse Problems and Numerical Analysis 2026.3.14
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Global quantitative uniqueness of continuation for Schrödinger equations with unbounded potentials Invited International conference
Hiroshi Takase
RIMS Symposium (Open) Inverse problems for partial differential equations and related areas 2026.1.14
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Stability in elliptic inverse problems for determining boundary functions International conference
Hiroshi Takase
China-Japan Joint Workshop on Practical Inverse Problems Based on Interdisciplinary and/or Industry-Academia Collaboration 2025.10.15 Institute of Mathematics for Industry, Kyushu University
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Global quantitative unique continuation for the Schrödinger equation with unbounded potential Invited International conference
Hiroshi Takase
The 8th Joint Conference of A3 Foresight Program on Computational and Applied Mathematics 2025.8.14
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Lipschitz stability for Cauchy problems of elliptic equations and extensions to evolution equations Invited International conference
Hiroshi Takase
Optimal Control and Inverse Problems in PDE Theory 2025.6.13
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Lipschitz stability for Cauchy problems of elliptic equations and applications to evolution equations Invited International conference
Hiroshi Takase
The 8th Young Scholar Symposium, East Asia Section of Inverse Problems International Association 2024.11.17
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Lipschitz stability estimate for an inverse problem related to unique continuation Invited
Workshop for young scholars Control and inverse problems on waves, oscillations and flows - Mathematical analysis and computational methods - 2024.9.24
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Lipschitz stability for Cauchy problems of elliptic equations Invited International conference
Hiroshi Takase
Finland-Japan Workshop in Industrial and Applied Mathematics 2024.8.27
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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 2024.6.16
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Global Lipschitz stability for inverse problems of waves on Lorentzian manifolds Invited International conference
Hiroshi Takase
The 11th International Conference Inverse Problems: Modeling and Simulation 2024.5.28
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Inverse source problems for wave equations with inverse square potentials Invited International conference
Hiroshi Takase
2024 Japan-Taiwan Joint Workshop on Numerical Analysis and Inverse Problems 2024.3.10
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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 2024.1.24
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Lipschitz stability for inverse source problems of waves on Lorentzian manifolds
Hiroshi Takase
11th Applied Inverse Problems Conference 2023.9.7
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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) 2023.8.23
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Inverse problems for first-order hyperbolic equations
Hiroshi Takase
The 59th ANZIAM Conference 2023.2.9
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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” 2022.12.5
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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 」 2022.11.4
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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 2022.9.10
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Inverse source problems for wave equations on Lorentzian manifolds Invited
Hiroshi Takase
10th International Conference “Inverse Problems: Modeling and Simulation” 2022.5.23
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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” 2022.1.5
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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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Global Lipschitz stability for inverse source problems of Lorentzian wave equations Invited
Hiroshi Takase
Joint Fudan - RICAM Seminar on Inverse Problems 2023.11.22
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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 2023.4.21
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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 2022.7.21
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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 2022.6.24
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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 2020.12.18
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
髙瀬裕志
Research Projects
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新たな条件付き安定性理論の探求と逆問題への応用 International coauthorship
Grant number：25K17280 2025.04 - 2028.03
日本学術振興会 科学研究費助成事業 若手研究
高瀬 裕志
Authorship：Principal investigator Grant type：Competitive
Grant amount：\4810000 （ Direct expense: \3700000 、 Indirect expense：\1110000 ）
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Inverse problem theory for innovation of detection methods International coauthorship
Grant number：23KK0049 2023.09 - 2028.03
Japan Society for the Promotion of Science 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
Authorship：Coinvestigator(s) Grant type：Competitive
Grant amount：\20280000 （ Direct expense: \15600000 、 Indirect expense：\4680000 ）
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Inverse problems for degenerate hyperbolic partial differential equations on manifolds International coauthorship
Grant number：22K20340 2022.08 - 2024.03
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity Start-up Grant-in-Aid for Research Activity Start-up
Takase Hiroshi
Authorship：Principal investigator Grant type：Competitive
Grant amount：\2860000 （ Direct expense: \2200000 、 Indirect expense：\660000 ）
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 International coauthorship
Grant number：20J11497 2020.04 - 2022.03
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows Grant-in-Aid for JSPS Fellows
Hiroshi Takase
Authorship：Principal investigator Grant type：Competitive
Grant amount：\1900000 （ Direct expense: \1900000 ）
まず空間二次元における波動方程式のコーシー問題を考察した．時間軸も含めた3次元ユークリッド空間上の円柱面に斉次コーシーデータを与えたときのコーシー問題に対し，解の一意性が破綻する非自明な解が無限個存在することを証明した．円柱面の近傍の有界な円環領域を加算無限個に分割し，ベッセル関数の漸近解析と１の分割を用いて構成的に証明した．さらに構成した無限個の非一意解が，光学迷彩の一種であるクローキング技術に応用できる可能性を示唆した．
<BR>
次に時間依存する係数を含む一階の非退化双曲型偏微分方程式の波源項決定逆問題及び係数決定逆問題に対し，大域リプシッツ型安定性を証明した．係数が生成するベクトル場に対し散逸性という概念を新たに導入しカーレマン評価を確立した．しかしながら本成果は係数の時間依存性に強い仮定を課しており，これを取り除けるか検証することは今後の課題である．また主要部の係数が時間のみに依存する一階の退化双曲型偏微分方程式に対し，カーレマン評価を確立し可観測性評価を証明した．方程式及びその解を正則性を保ったまま時間負方向へ拡張することで，退化型方程式に対しても大域カーレマン評価を確立する手法を開発した．
<BR>
最後に主要部が連立する強連立型の一階の対称双曲型偏微分方程式に対し，カーレマン評価を確立し可観測性評価を証明した．もともと二階の方程式に対し用いられる第二パラメーターを導入することで大域カーレマン評価を確立し，強連立型方程式においても従来の手法が適用できることを解明した．
Academic Activities
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China-Japan Joint Workshop on Practical Inverse Problems Based on Interdisciplinary and/or Industry-Academia Collaboration International contribution
Role(s)：Planning, management, etc.
Institute of Mathematics for Industry （ Fukuoka ） 2025.10.14 - 2025.10.17