Singularity of solutions and stationary problems for nonlinear parabolic equations
| Project/Area Number |
17K05333
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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 | Hiroshima University (2020)
Ehime University (2017-2019) |
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Principal Investigator |
Naito Yuki 広島大学, 先進理工系科学研究科(理), 教授 (10231458)
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| Co-Investigator(Kenkyū-buntansha) |
猪奥 倫左 東北大学, 理学研究科, 准教授 (50624607)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 非線形解析 / 非線形楕円型方程式 / 非線形熱方程式 / 自己相似解 / 特異解 / 楕円型偏微分方程式 / 放物型偏微分方程式 / 定常問題 |
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| Outline of Final Research Achievements |
We showed the existencde and the uniquness of the singular solutions to semilinear elliptic partial differential equations with Sobolev super-critical nonlinearity. We also showed the convergence of regular solutions to the singular solution.
We consider positive solutions of the semilinear heat equation with supercritical power nonlinearity, and construct peaking solutions by connecting a backward selfsimilar solution with a forward self-similar solution. In particular, we show the existence of incomplete blow-up solutions with blow-up profile above the singular steady state.
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| Academic Significance and Societal Importance of the Research Achievements |
非線形楕円型偏微分方程式に対する境界値問題に対して、特異解から分岐構造を解析するという新たな手法の確立が期待できる。
特異定常解より大きな爆発形状をもつ不完全爆発解の構成により「爆発形状が特異定常解より大きければ完全爆発である」という直感を裏切る結果が得られた。これにより、非線形熱方程式における爆発問題において新たな進展が期待できる。
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Report
(5 results)
Research Products
(40 results)
