IUMJ

Title: Seminlinear parabolic equation on bounded domain with critical Sobolev exponent

Authors: Takashi Suzuki

Issue: Volume 57 (2008), Issue 7, 3365-3396

Abstract:

This paper is concerned with the semilinear parabolic equation $u_t - \Delta u = |u|^{p-1}u$ on bounded domain in $\mathbb{R}^n$ with the critical Sobolev exponent $p = (n+2)/(n-2)$. We study positive solutions and classify their global in time behavior. Particularly, the blowup in infinite time is shown when $\Omega$ is convex and symmetric.