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2002 On some Dirichlet and Cauchy problems for a singular diffusion equation
Kin Ming Hui
Differential Integral Equations 15(7): 769-804 (2002).

Abstract

We will prove the existence and uniqueness of solutions of the Dirichlet problem $u_t=\Delta$ log $u$, $u>0$, in $\Omega\times (0,\infty)$, $u=g$ on $\partial \Omega\times (0,\infty)$, $u(x,0)=u_0(x)\ge 0$ on $\Omega$ where $\Omega\subset R^n$ is a smooth bounded domain. We will also prove the local and global existence and uniqueness of maximal solutions of the above equation in $R^n\times (0,\infty )$ for $n\ge 3$ under very general condition on $u_0$ and we will prove finite time extinction of solution for $u_0\in L_{loc}^{\infty}(R^n)$ satisfying $0\le u_0(x)\le C/|x|^2$ for all $|x|\ge R_0$ for some constants $C>0$, $R_0>0$.

Citation

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Kin Ming Hui. "On some Dirichlet and Cauchy problems for a singular diffusion equation." Differential Integral Equations 15 (7) 769 - 804, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1020.35038
MathSciNet: MR1895566

Subjects:
Primary: 35K55
Secondary: 35B40 , 35D05 , 35K65

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 7 • 2002
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