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

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.

Keywords

• Cross-diffusion
• global solution
• gradient estimates
• stability