Analysis on moving singularities in evolution equations
| Project/Area Number |
16K13769
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
YANAGIDA Eiji 東京工業大学, 理学院, 教授 (80174548)
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| Co-Investigator(Kenkyū-buntansha) |
菅 徹 大阪府立大学, 理学(系)研究科(研究院), 准教授 (60647270)
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| Research Collaborator |
KHIN Phyu Phyu Htoo
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 発展方程式 / 偏微分方程式 / 特異点 / 非線形解析 / 臨界指数 / 分岐 / 動的特異点 / 漸近解析 / 特異性 |
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| Outline of Final Research Achievements |
In this project, we study the existence of solutions with moving singularities for some linear and nonlinear partial differential equations, and examine the profile and dynamics of such solutions. More specifically, for the Fujita equation, the absorption equation, the linear heat equation with a dynamic potential, and a singular diffusion equations, and investigate the conditions for the existence of singular solutions and asymptotic profile near singularities. By these studies, it is shown that the importance of some critical exponents and the Holder exponent of the motion of the singularity are crucial.
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| Academic Significance and Societal Importance of the Research Achievements |
特異点の研究は古くからあり、特に非線形楕円型偏微分方程式の研究はかなり進んでいる。しかしながら、放物型偏微分方程式における移動特異点は、数学的には自然な対象であるにもかかわらず、研究はまだ始まったばかりである。この計画で得られた成果は今後の移動特異点理論の基礎となるものであり、偏微分方程式論や幾何学への応用も含めて、今後さらに発展するものと期待される。
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Report
(4 results)
Research Products
(27 results)
