2012 Fiscal Year Final Research Report
Asymptotic behavior of solutions for evolution equations involving nonlinear Laplacians
| Project/Area Number |
22740093
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Kobe University (2011-2012)
Shibaura Institute of Technology (2010) |
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Principal Investigator |
AKAGI Goro 神戸大学, 大学院・システム情報学研究科, 准教授 (60360202)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 非線型解析 / 発展方程式 / 解の漸近挙動 / 偏微分方程式 / 関数解析 |
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| Research Abstract |
In various nonlinear problems, we often encounter nonlinear elliptic operators as modified forms of the classical (linear) Laplacian. In this research, we consider evolution equations governed by such nonlinear operators and investigate asymptotic behavior of solutions and their mechanism. More precisely, we revealed long-time behavior of solutions for diffusion-type equations involving p(x)-Laplacians with variable exponents and the infinity-Laplacian, and moreover, we also established a novel theory of stability analysis of asymptotic profiles for vanishing (in finite time) solutions of fast diffusion equations.
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