2013 Fiscal Year Final Research Report
Blow-up problem for a nonlinear diffusion equation and its diffusion coefficient
| Project/Area Number |
24840027
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Keywords | 非線形偏微分方程式 / 爆発問題 / 爆発集合 / 拡散係数 / 解の形状 |
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| Research Abstract |
This research program is devoted to the study of the relationship between the blow-up problem for a nonlinear heat equation and the diffusion coefficient. In particular, I have studied the characterization of the location of the blow-up set under a small diffusion situation.
In the first year of this program, I applied the results of the blow-up problem with small diffusion, and proved the non-existence of the radially symmetric solution which blows up on the boundary for a nonlinear heat equation on an annulus.
In the final year of this program, I have studied the blow-up problem for a superlinear heat equation with general nonlinearity including exponential nonlinearity. In particular, I characterized the location of the blow-up set of solutions with small diffusion.
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