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.
Show me the PDF file (276 KB), TEX file, and other files for this article.
|Shenghu Xu |
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China
Return to the EJDE web page