Parabolic Liouville-type theorems via their elliptic counterparts

Pages: 1206 - 1213, Issue Special, September 2011

 Abstract        Full Text (303.9K)              

Pavol Quittner - Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovak Republic (email)
Philippe Souplet - Université Paris 13, CNRS UMR 7539, Laboratoire Analyse, Géométrie et Applications, 99, avenue J.-B. Clément, 93430 Villetaneuse, France (email)

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

Received: July 2010;      Revised: July 2011;      Published: October 2011.