Solvability and long time behavior of nonlinear reaction-diffusion equations with Robin boundary condition
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.108, pp.1-13, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 108
- Publication Date: 2014
- Doi Number: 10.1016/j.na.2014.05.008
- Journal Name: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.1-13
- Hacettepe University Affiliated: Yes
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.