Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 158, pp. 1-7.

Title: Solution to nonlinear gradient dependent systems with a balance law

Authors: Zoubir Dahmani (Univ. of Mostaganem, Algeria)
         Sebti  Kerbal (Sultan Qaboos University, Oman)

Abstract: 
 In this paper, we are concerned with the initial boundary value
 problem (IBVP) and with the Cauchy problem to the reaction-diffusion
 system
 $$ \displaylines{
 u_t-\Delta u    = -u^n |\nabla v |^p,\cr
 v_t-d \Delta v  =  u^n |\nabla v|^p,
 }$$
 where $1\leq p\leq 2$, d and n are positive real numbers.
 Results on the existence and large-time behavior
 of the solutions are presented. 
 
Submitted April 15, 2007. Published November 21, 2007.
Math Subject Classifications: 35B40, 35B50, 35K57.
Key Words: Reaction-diffusion systems; global existence; asymptotic behavior;
           maximum principle.