, Volume 320, Issue 2, pp 299-305

Universal bound for global positive solutions of a superlinear parabolic problem

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Abstract.

We prove universal a priori estimates of global positive solutions of the parabolic problem \(u_t=\Delta u+u^p\) in \(\Omega\times(0,\infty)\) , \(u=0\) on \(\partial\Omega\times(0,\infty)\) . Here \(\Omega\) is a bounded domain in \({\mathbb R}^n\) , \(n\leq3\) , \(p>1\) and p < 5 if n=3.

Received April 6, 2000 / Accepted September 21, 2000 / Published online February 5, 2001