2023 Fiscal Year Final Research Report
Studies on variational problems, optimization problems and nonlinear partial differential equations
| Project/Area Number |
19K03587
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12020:Mathematical analysis-related
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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| Keywords | 変分問題 / パターン形成 / 非線形シュレディンガー方程式 / 逆問題 / 凝集現象 / 漸近挙動 / メトリックグラフ |
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| Outline of Final Research Achievements |
In this study, we treated several nonlinear elliptic boundary value problems associated with corresponding pattern formation phenomena, for example FitzHugh-Nagumo system, Schanekenberg model, Keller-Segel chemotaxis model. Moreover, we also studied an inverse boundary value problem for the magnetic Shroedinger equation and several nonlinear elliptic problem on compact metric graphs.
We obtained results to clarify the relationship between the network structure of the compact metric graphs and the structure of solutions.
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| Free Research Field |
変分問題と非線形偏微分方程式
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| Academic Significance and Societal Importance of the Research Achievements |
様々なパターン形成問題の定常パターン形成のメカニズムを非線形楕円型微分方程式で記述される数理モデルの精密な数学解析を通して、理解することができるという点で、学術的意義は深いと考えている。様々な複雑な自然現象の基本的なメカニズムが単純な数理モデルに内在することを示しているという点で、数学解析の持つ社会的意義は大きいと思われる。
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