Okabe Shinya

オカベシンヤ | Okabe Shinya

Affiliation and department：
Job title： Associate Professor

Research field (1)： Mathematical analysis

Research keywords (2)：変分法 , 偏微分方程式論

Research theme for competitive and other funds (14)：

2022 - 2026 Mathematical and numerical analysis of Sobolev gradient flows appearing in interface and materials science
2021 - 2026 Analysis on singularities of higher order geometric gradient flows
2020 - 2025 New development on higher order elliptic and parabolic PDEs -- cooperation between harmonic analysis and geometric analysis
2019 - 2024 Systematical geometric analysis and asymptotic analysis for evolution equations
2019 - 2022 曲線がなす距離空間におけるエネルギー勾配流の構成とその応用

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Papers (31)：

Hans-Christoph Grunau, Shinya Okabe. Willmore Obstacle Problems under Dirichlet Boundary Conditions. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. 2023. 1415-1462
Shinya Okabe, Glen Wheeler. The p-elastic flow for planar closed curves with constant parametrization. Journal de Mathématiques Pures et Appliquées. 2023. 173. 1-42
Kazuhiro Ishige, Shinya Okabe, Tokushi Sato. Existence of nonminimal solutions to an inhomogeneous elliptic equation with supercritical nonlinearity. Advanced Nonlinear Studies. 2023. 23. 1
Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe. Existence of solutions to nonlinear parabolic equations via majorant integral kernel. Nonlinear Analysis. 2022. 223. 113025-113025
Kazuhiro Ishige, Shinya Okabe, Tokushi Sato. Thresholds for the existence of solutions to inhomogeneous elliptic equations with general exponential nonlinearity. Advances in Nonlinear Analysis. 2022. 11. 1. 968-992

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MISC (9)：

Shinya Okabe. $H^2$(ds)-Sobolev gradient flow for the modified elastic energy. RIMS Kokyuroku Innovation of the theory for evolution equations: developments via cross-disciplinary studies. 2024. 2277. 79-89
岡部真也. 高階放物型問題に対する変分的時間離散近似解法. 応用数学勉強会レクチャーノート. 2021. 1-81
Shinya Okabe. Construction of solutions to a fourth order parabolic obstacle problem. RIMS Kokyuroku. 2014. 1896. 12-25
Shinya Okabe. Remarks on the motion of non-closed planar curves governed by shortening-straightening flow. 数理解析研究所講究録-現象の数理解析へ向けた非線形発展方程式とその周辺-. 2011. 1746. 34-48
Shinya Okabe, Takashi Suzuki, Syuji Yoshikawa. 形状記憶合金ワイヤーの運動を記述する熱弾性方程式の導出. 数理解析研究所講究録-非線形発展方程式と現象の数理-. 2010. 1693. 1-10

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Lectures and oral presentations (97)：

Dynamical approach to a generalized isoperimetric inequality
(2024 OIST Workshop, Geometric Aspects of Partial Differential Equations 2024)
Recent advances in Sobolev gradient flows for curves
(Euro-Japan Conference on Nonlinear Diffusions 2023)
数学と医療の交叉点〜癌治療と関わるある数理モデル〜
(日本数学会2023年度秋季総合分科会市民講演会 2023)
Convergence of Sobolev gradient trajectories to elastica
(Frontiers of gradient flows: well-posedness, asymptotics, singular limits 2023)
Convergence of Sobolev gradient trajectories to elastica
(2022)

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Education (3)：

Professional career (1)：

Work history (3)：

Awards (1)：

Association Membership(s) (1)：

日本数学会

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