Global solutions to cross diffusion parabolic systems on 2D domains
Dung Le, Vu T. Nguyen · Proceedings of the American Mathematical Society · 2015
This paper studies global existence of cross diffusion systems on 2-dimensional domains. We assume a quadratic growth on the reaction part and show that a solution exists globally if and only if its total reaction energy does not blow up in finite time. Applications to cross diffusion systems with Lotka-Volterra reaction are presented.