| Project/Area Number |
17K05340
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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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| Research Field |
Mathematical analysis
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| Research Institution | Kanagawa University (2020-2021)
Numazu National College of Technology (2017-2019) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 自由境界問題 / 反応拡散方程式 / 多安定型 / テラス解 / propagating terrace / 進行波 / 球対称 / 放物型方程式 / 解の形状 |
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| Outline of Final Research Achievements |
My research deal with a free boundary problem of reaction diffusion equation. This problem models spreading phenomena of invasive biological of chemical species. This model has been proposed by Du and Lin(2010) and a lot of researchers have studied them after the appearance of the study of Du and Lin. In my study, I discussed a reaction diffusion equation with a positive bistable nonlinear term which has two positive stable equilibrium and revealed detailed asymptotic profile s of solution over the whole domain. In particular, I have found under suitable condition, the solution approaches so-called propagating terrace(a system of stacked traveling fonts and semi-wave front).
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| Academic Significance and Societal Importance of the Research Achievements |
反応拡散方程式の自由境界問題は外来種が生息領域を拡大する現象のモデルに端を発しており、現実問題の観点からもその理論的解析は重要である。本研究で扱うpositive bistable型の非線形項は北アメリカに住む森林害虫の個体数密度のダイナミクスのモデルに現れる非線形項である。数学的には反応拡散方程式の自由境界問題における解の定義域全体での漸近的形状を調べる手法を確立したといえる。今後，生態系のしくみ，さらには環境保全にいたるまで課題解決のひとつの手がかりとなりうる。
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