Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 55, Issue 1, pp 28–31

Monotonicity of solutions and blow-up for semilinear parabolic equations with nonlinear memory

Original paper

DOI: 10.1007/s00033-003-1158-0

Cite this article as:
Souplet, P. Z. angew. Math. Phys. (2004) 55: 28. doi:10.1007/s00033-003-1158-0

Abstract

We show the existence of monotone in time solutions for a semilinear parabolic equation with memory. The blow-up rate estimate of the solution is known to be a consequence of the monotonicity property.

Mathematics Subject Classification (2000):

35K6035B4035R10

Keywords.

Nonlocal parabolic equationnonlinear memoryblow-up ratemonotonicity

Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Département de Mathématiques, Université de Picardie, INSSETSt-QuentinFrance
  2. 2.Laboratoire de Mathématiques Appliquées, UMR CNRS 7641, Université de VersaillesVersaillesFrance