Parabolic Liouville-type theorems via their elliptic counterparts

Pavol Quittner; Philippe Souplet

doi:10.3934/proc.2011.2011.1206

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2011, Volume 2011: 1206-1213. Doi: 10.3934/proc.2011.2011.1206 open access

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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: August 2017

Abstract / Introduction Related Papers Cited by

Abstract

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.

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