Abstract and Applied Analysis 
Volume 2003 (2003), Issue 9, Pages 521-538
doi:10.1155/S1085337503210022

Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation

Nikos Karachalios,1 Nikos Stavrakakis,2 and Pavlos Xanthopoulos2

 1Department of Statistics and Actuarial Science, School of Sciences, University of the Aegean, Samos, Karlovassi 83200, Greece
2Department of Mathematics, National Technical University, Zografou Campus, Athens 157 80, Greece
Received 3 September 2002

Abstract

We consider a nonlinear parabolic equation involving nonmonotone diffusion. Existence and uniqueness of solutions are obtained, employing methods for semibounded evolution equations. Also shown is the existence of a global attractor for the corresponding dynamical system.