Seminlinear parabolic equation on bounded domain with critical Sobolev exponent Takashi Suzuki 35K55parabolic equationcritical Sobolev exponentblowup rateblowup in infinite time 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. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3269 10.1512/iumj.2008.57.3269 en Indiana Univ. Math. J. 57 (2008) 3365 - 3396 state-of-the-art mathematics http://iumj.org/access/