Semilinear Parabolic Equation on Bounded Domain with Critical Sobolev Exponent

摘要

This paper is concerned with the semilinear parabolic equation u(t) - Delta u = vertical bar u vertical bar(p-1)u on bounded domain in 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.