Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 134, pp. 1-16.

Title: Asymptotic behaviour for a diffusion equation governed
       by nonlocal interactions

Author: Armel Andami Ovono (L.A.M.F.A CNRS, France)

Abstract:
 In this article, we study the asymptotic behaviour of a nonlocal
 nonlinear parabolic equation governed by a parameter.
 After giving the  existence of unique branch of solutions composed
 by stable solutions in stationary case, we gives for the parabolic
 problem  $L^\infty$ estimates  of solution based on using the
 Moser iterations and existence of global attractor. We finish our
 study by the issue of asymptotic behaviour in some cases when
 $t\to \infty$.
 	 
Submitted March 9, 2010. Published September 20, 2010.
Math Subject Classifications: 35B35, 35B40, 35B51.
Key Words: Comparison principle; nonlocal diffusion;
           branch of solutions; asymptotic behaviour.