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.
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Received April 6, 2000 / Accepted September 21, 2000 / Published online February 5, 2001
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Quittner, P. Universal bound for global positive solutions of a superlinear parabolic problem. Math Ann 320, 299–305 (2001). https://doi.org/10.1007/PL00004475
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DOI: https://doi.org/10.1007/PL00004475