Global solutions to cross diffusion parabolic systems on 2D domains

Le, Dung; Nguyen, Vu

doi:10.1090/S0002-9939-2015-12501-4

Global solutions to cross diffusion parabolic systems on 2D domains
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by Dung Le and Vu Thanh Nguyen PDF

Proc. Amer. Math. Soc. 143 (2015), 2999-3010 Request permission

Abstract:

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.

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