Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 1
ASYMPTOTIC BEHAVIOR OF THE NON-AUTONOMOUS REACTION-DIFFUSION EQUATION WITH ROBIN BOUNDARY CONDITION
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 422–440
- DOI
- —
Abstract
In this paper, we investigate the long-time behavior of the timedependent reaction-di§usion equation ut u+a(x)juj ub(x)juj u = h(x; t) with Robin boundary condition. We begin this paper with the existence and uniqueness results of the solution to the problem. For the asymptotic behavior, we Örstly prove the existence of an absorbing set in W1 2 ( ) L+2( ). The existence of a uniform attractor is obtained in W1 2 ( ) L+2(