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2011, 2011(Special): 1206-1213. doi: 10.3934/proc.2011.2011.1206

Parabolic Liouville-type theorems via their elliptic counterparts

Pavol Quittner 1, and  Philippe Souplet 2,

1. 

Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislava
2. 

Université Paris 13, CNRS UMR 7539, Laboratoire Analyse, Géométrie et Applications, 99, avenue J.-B. Clément, 93430 Villetaneuse

Received  July 2010 Revised  July 2011 Published  October 2011

We study several parabolic problems with gradient structure and show how the nonexistence of entire stationary solutions can be used in the proof of nonexistence of entire time-dependent solutions.
Keywords: nonlinear parabolic problems; Liouville theorems.
Mathematics Subject Classification: Primary: 35K55, 35K57, 35B40; Secondary: 35B45.
Citation: Pavol Quittner, Philippe Souplet. Parabolic Liouville-type theorems via their elliptic counterparts. Conference Publications, 2011, 2011 (Special) : 1206-1213. doi: 10.3934/proc.2011.2011.1206
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