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2003 Uniqueness and nonuniqueness for the porous medium equation with non linear boundary conditions
Carmen Cortazar, Manuel Elgueta, Julio D. Rossi
Differential Integral Equations 16(10): 1215-1222 (2003).

Abstract

We study the uniqueness problem for nonnegative solutions of $u_t=\Delta u^m$ in $\Omega \times [0,T)$, $-\frac{\partial u^m}{\partial \hat{n}}(x,t)=u^{\lambda}(x,t)$ on $\partial \Omega \times (0,T)$ and $u(x,0) \equiv 0$ on $\Omega$ where $m > 1$, $\lambda \ge 1$, and $\Omega$ is a bounded domain with smooth boundary in $\mathbf {R}^N$. We prove that the solution $u \equiv 0$ is unique if and only if $2\lambda \geq m+1$.

Citation

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Carmen Cortazar. Manuel Elgueta. Julio D. Rossi. "Uniqueness and nonuniqueness for the porous medium equation with non linear boundary conditions." Differential Integral Equations 16 (10) 1215 - 1222, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1073.35083
MathSciNet: MR2014807

Subjects:
Primary: 35K57
Secondary: 35K60 , 76S05

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 10 • 2003
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