| Abstract: |
| This talk is about the lifespan estimate for the heat equation
$u_t=\Delta u$ in a bounded domain $\Omega$ in $\mathbb{R}^{n}(n\geq 2)$ with positive initial data $u_{0}$ and partial nonlinear radiation boundary conditions. First, the local existence and uniqueness of the classical solution will be discussed. Secondly, both upper and lower bounds of the lifespan will be shown. Finally, the asymptotic behavior of the bounds concerning the nonlinearity power $q$, the initial data $u_{0}$ and the area of the boundary part where the nonlinear radiation occurs will be explored. This is a joint work with Zhengfang Zhou. |
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