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Stabilization of solutions of weakly singular quenching problems

Authors: Marek Fila, Howard A. Levine and Juan L. Vázquez
Journal: Proc. Amer. Math. Soc. 119 (1993), 555-559
MSC: Primary 35K60; Secondary 35B65, 35D05
MathSciNet review: 1174490
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Abstract: In this paper we prove that if $ 0 < \beta < 1,\;D \subset {R^N}$ is bounded, and $ \lambda > 0$, then every element of the $ \omega $-limit set of weak solutions of

\begin{displaymath}\begin{array}{*{20}{c}} {{u_t} - \Delta u + \lambda {u^{ - \b... ...\times \{ 0\} \hfill \\ \end{gathered} \right.} \\ \end{array} \end{displaymath}

is a weak stationary solution of this problem. A consequence of this is that if $ D$ is a ball, $ \lambda $ is sufficiently small, and $ {u_0}$ is a radial, then the set $ \{ (x,t)\vert u = 0\} $ is a bounded subset of $ D \times [0,\infty )$.

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Article copyright: © Copyright 1993 American Mathematical Society

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