Solvability and long time behavior of nonlinear reaction-diffusion equations with Robin boundary condition


ÖZTÜRK E. , Soltanov K. N.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.108, pp.1-13, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 108
  • Publication Date: 2014
  • Doi Number: 10.1016/j.na.2014.05.008
  • Title of Journal : NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Page Numbers: pp.1-13

Abstract

In this paper, we investigate the long-time behavior and solvability of the reaction-diffusion equation, which has a polynomial growth nonlinearity of arbitrary order, with Robin boundary condition. We begin this paper with the existence and uniqueness of the solution to the problem. For the long-time behavior, we firstly prove the existence of an absorbing set in two different spaces. Secondly, for the autonomous case, the existence of a global attractor is obtained in W-2(1) (Omega) boolean AND L rho+2 (Omega). (C) 2014 Elsevier Ltd. All rights reserved.