Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 06, pp. 1-14.

Title: Existence of global solutions for a predator-prey
       model with cross-diffusion

Author: Shenghu Xu (Northwest Normal Univ., Lanzhou, China)

Abstract: 
 In this article, we prove the  existence of global classical solutions
 for a prey-predator model when the space dimension n<10. Under
 certain conditions on the coefficients of the reaction functions,
 the convergence of solutions is established for the system with
 large diffusion by constructing a Lyapunov function. 
 
Submitted October 13, 2007. Published January 12, 2008.
Math Subject Classifications: 35K57, 35B35, 92D25.
Key Words: Cross-diffusion; global solution; gradient estimates; stability.