Long-time extinction of solutions of some semilinear parabolic equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:238

Article

Belaud, Yves ; Shishkov, Andrey

关键词: nonlinear equation;    energy method;    vanishing solutions;    semi-classical analysis;   

DOI  :  10.1016/j.jde.2007.03.015

来源: Elsevier

【 摘 要 】

We study the long-time behavior of solutions of semilinear parabolic equation of the following type alu - Au +a(0)(x)u(q) = 0 where a(0)(x) >= d(0) exp(-omega vertical bar x vertical bar/vertical bar x vertical bar(2)), do > 0, 1 > q > 0, and omega is a positive continuous radial function. We give a Dini-like condition on the function to by two different methods which implies that any solution of the above equation vanishes in a finite time. The first one is a variant of a local energy method and the second one is derived from semi-classical limits of some Schrodinger operators. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free