Compact traveling waves for mean-curvature flow with driving force
| Project/Area Number |
18K13458
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Okayama University |
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Principal Investigator |
MONOBE HARUNORI 岡山大学, 異分野基礎科学研究所, 特任准教授 (20635809)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 平均曲率流方程式 / 進行波解 / 界面方程式 |
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| Outline of Final Research Achievements |
We studied the mean-curvature flow with driving force which is derived from some mathematical models, such as cell-locomotion and droplet motion. As a result, we have the following results : (1) if the driving force is positive, there exists a unique compact traveling wave (CTW) solutions. (2) if the driving force is negative, there does not exists any CTW solutions. (3). if the driving force is sign-changing and some conditions are satisfied, there exists a unique CTW solutions. (4). if CTW exists, every CTW is convex and unstable.
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| Academic Significance and Societal Importance of the Research Achievements |
偏微分方程式で記述される数理モデルにおいて、スポット状パターンの発生メカニズムは未だ明確にはわかっておらず、現在もモデル構築の際は、経験則に頼るところが多い。このため、より複雑な形状のパターンへの解析が滞っている。本研究成果は、スポット状の物質が移動する現象の数理モデルを考えた時に、その構築方法や解の振る舞いの解析の手助けになると考えられる。
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Report
(5 results)
Research Products
(28 results)
