Infinite-Time Quenching in a Fast Diffusion Equation with Strong Absorption期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Infinite-Time Quenching in a Fast Diffusion Equation with Strong Absorption

Authors:	Michael Winkler

Institution:	(1) Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava, Slovakia

Abstract:	This work is concerned with the fast diffusion equation $u_{t} = \Delta u^{m}-u^{\kappa} \,{\rm in}\,{\mathbb{R}}^{n}$ , where 0 < m < 1 and κ < 1. A global positive solution is said to quench regularly in infinite time if $u(x_{k}, t_{k}) \rightarrow 0$ for some bounded sequence $(x_{k})_{k\in{\mathbb{N}}}$ and some $t_{k} \rightarrow \infty$ , and if ${\rm sup}_{(x,t)\in K \times(0,\infty)} u(x, t) < \infty$ for all compact $K \subset\subset {\mathbb{R}}^{n}$ . It is shown that such regular quenching in infinite time occurs for a large class of initial data if κ > m , whereas it is impossible in one space dimension when κ < −m and the solution is radially symmetric and nondecreasing for x > 0.

Keywords:	" target="_blank"> Fast diffusion strong absorption quenching in infinite time
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