2022 Fiscal Year Final Research Report
Stationary problem of spatially inhomogeneous reaction diffusion equations
| Project/Area Number |
18K03358
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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 University of Marine Science and Technology |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | 特異摂動問題 / スパイク / 遷移層 / 解の大域的分岐構造 |
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| Outline of Final Research Achievements |
We studied the model of gene frequency introduced by Nagylaki in population genetics. This model is expressed using the reaction-diffusion equation, and the coefficient g(x) representing the spatial dependence of the nonlinear term is assumed to change sign. Specifically, the nonlinear term is g(x)u^2 (1-u). Two conjectures about the number of solutions of Lou-Nagylaki have been resolved negatively. The results were announced to Rapporteur (2020) and Rapporteur-Su (2020).
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| Free Research Field |
非線形反応拡散方程式
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| Academic Significance and Societal Importance of the Research Achievements |
本方程式の生物学的な意義に加え，数学的な意義は次のようである．非線形項が符号を変えるようなロジスティックタイプの方程式の正値定常解の分岐構造を研究は1970年代から国内外でさかんに行われてきた．非線形項が符号を変えない場合には,数えきれないほどの先行研究があるが，非線形項が符号を変える場合には変えない場合に比べて国内外でも研究が始まったばかりと言ってよく，その解の挙動は数学的にも複雑で興味深い．
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