Singular solutions for semi-linear parabolic equations on nonsmooth domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:333

Article

Riahi, Lotfi

关键词: semi-linear parabolic equation;    kato class;    singular solution;    nonsmooth domains;   

DOI  :  10.1016/j.jmaa.2006.11.035

来源: Elsevier

【 摘 要 】

We prove the existence of positive singular solutions for the semi-linear parabolic equation Delta(x)u - (partial derivative)/(partial derivative t) u+ mu u(P) = 0 on Omega = D x ]0, infinity[, where p > 1, D is a bounded NTA-domain in R-n, n > 2, and mu is in a general class of signed Radon measures on D covering the elliptic Kato class of potentials adopted by Zhang and Zhao. A new proof of the result based on a simple fixed point theorem is also given. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free