Local and global properties of solutions of heat equation with superlinear absorption

Tai Nguyen Phuoc; Laurent Veron

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arXiv · 1002.4737

Local and global properties of solutions of heat equation with superlinear absorption

Tai Nguyen Phuoc·Laurent Veron

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Abstract

We study the limit, when $k\to\infty$ of solutions of $u_t-\Delta u+f(u)=0$ in $R^N\times(0,\infty)$ with initial data $k\gd$, when $f$ is a positive increasing function. We prove that there exist essentially three types of possible behaviour according $f^{-1}$ and $F^{-1/2}$ belong or not to $L^1(1,\infty)$, where $F(t)=\int_0^t f(s)ds$. We emphasize the case where f(u)=u((\ln u+1))^{\alpha}. We use these results for giving a general result on the existence of the initial trace and some non-uniqueness results for regular solutions with unbounded initial data.

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Tai Nguyen Phuoc, Laurent Veron. 2010-02-25. Local and global properties of solutions of heat equation with superlinear absorption. https://arxiv.org/abs/1002.4737

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