Global existence of solutions for a reaction-diffusion system

Abstract

We show the global existence of solutions of a reaction-diffusion system with the nonlinear terms $|x|^{\sigma_j}u^{p_j}v^{q_j}$. The proof is based on the existence of supersolutions and the comparison principle. We also prove that uniqueness of the global solutions holds in the superlinear case by contraction argument. Our conditions for the global existence are optimal in view of the nonexistence results proved by Yamauchi [12].