Mathematische Annalen

, Volume 320, Issue 2, pp 299–305

Universal bound for global positive solutions of a superlinear parabolic problem

  • Pavol Quittner
Original article

DOI: 10.1007/PL00004475

Cite this article as:
Quittner, P. Math Ann (2001) 320: 299. doi:10.1007/PL00004475
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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.

Mathematics Subject Classification (2000): 35B45, 35K60

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Pavol Quittner
    • 1
  1. 1.Institute of Applied Mathematics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovakia (e-mail: quittner@fmph.uniba.sk) SK