Critical exponent and the behavior of solutions to nonlinear parabolic partial differential equations
| Project/Area Number |
26400171
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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 | Ehime University |
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Principal Investigator |
Yuki Naito 愛媛大学, 理工学研究科(理学系), 教授 (10231458)
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| Co-Investigator(Kenkyū-buntansha) |
石井 克幸 神戸大学, 海事科学研究科, 教授 (40232227)
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| Co-Investigator(Renkei-kenkyūsha) |
Yanagida Eiji 東京工業大学, 大学院理工学研究科, 教授 (80174548)
Ishwata Michinori 大阪大学, 大学院基礎工学研究科, 教授 (30350458)
Senba Takasi 九州工業大学, 大学院工学研究科, 教授 (30196985)
Kajikiya Ryuji 佐賀大学, 大学院工学研究科, 教授 (10183261)
Yoshikawa Syuji 愛媛大学, 大学院理工学研究科, 准教授 (80435461)
Ioku Norisuke 愛媛大学, 大学院理工学研究科, 助教 (50624607)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 非線形熱方程式 / 定常問題 / 自己相似解 / 優Sobolev臨界 / 非線形解析 / 楕円型偏微分方程式 / Liouville 型定理 / A priori 評価 / 臨界指数 / 非線形偏微分方程式 / 分岐問題 / 放物型偏微分方程式 / 国際研究者交流：韓国 |
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| Outline of Final Research Achievements |
We consider the semilinear elliptic equation and study separation phenomena of positive radial solutions. With respect to intersection and separation, we establish a classification of the solution structures. We show that, under the suitable conditions, the equation has the structure of separation and possesses a singular solution as the upper limit of regular solutions. We also reveal that the equation changes its nature drastically across the critical exponent which is determined by the space dimension and the order of the behavior of the coefficient function. We consider the behavior of solutions to the Cauchy problem for a semilinear heat equation with supercritical nonlinearity. We study the convergence of solutions to steady states in a weighted norm, and show the global attractivity property of steady states. We also give its convergence rate for a class of initial data. Proofs are given by a comparison method based on matched asymptotic expansion.
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Report
(5 results)
Research Products
(39 results)
