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Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems

  • Juraj Földes Nashville
Article

Abstract

In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.

Keywords

a priori estimates Liouville theorems blow-up rate positive solution indefinite parabolic problem 

MSC 2010

35B09 35B44 35B45 35B53 35J61 35K59 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2011

Authors and Affiliations

  1. 1.NashvilleUSA
  2. 2.Vanderbilt UniversityNasvhilleUSA

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