2017 Fiscal Year Final Research Report
Studies on nonlinear partial differential equations via potential analysis
| Project/Area Number |
26400137
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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 |
Basic analysis
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
小野 太幹 福山大学, 人間文化学部, 准教授 (60289270)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | ポテンシャル論 / 偏微分方程式 / 実解析 |
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| Outline of Final Research Achievements |
We have investigated some relations among the dimension of a singular set, the growth rate of a solution and the removability of a singular set for the Laplace, p-Laplace, heat equations with nonlinear source or absorption terms, and obtained results which enable us to consider fractal sets as singular sets. Also, for semilinear heat equations in a Lipschitz domain, we have obtained results about the existence of positive solutions with isolated boundary singularities and a priori estimates for all positive solutions.
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| Free Research Field |
数物系科学
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