Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 07, pp. 1-5.

Title: Stabilization of solutions for semilinear parabolic systems 
       as $|x|\to \infty$
   
Author: Alexander Gladkov (Vitebsk State Univ., Belarus)

Abstract:
 We prove that solutions of the Cauchy problem for semilinear 
 parabolic systems converge to solutions of the Cauchy problem
 for a corresponding systems of ordinary differential equations,
 as $|x| \to \infty$.
 
Submitted October 13, 2008. Published January 06, 2009.
Math Subject Classifications: 35K55, 35K65.
Key Words: Semilinear parabolic systems; stabilization