Hokkaido University Preprint Series in Mathematics
We show the global existence of solutions of a reactiondiffusion system with the nonlinear terms |x|σjupj vqj . The proof is based on the existence of super-solutions 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 .