Generalized Result on Global Existence of Weak Solutions for Parabolic Reaction-Diffusion Systems

Abstract

In this paper, we study global existence of weak solutions for 2 × 2 parabolic reaction-diffusion systems with a full matrix of diffusion coefficients on a bounded domain, such as, we treat the main properties related: the positivity of the solutions and the total mass of the components are preserved with time. Moreover, we suppose that the non-linearities have critical growth with respect to the gradient. The technique used is based on compact semigroup methods and some estimates. Our objective is to show, under appropriate hypotheses, that the proposed model has a global solution with a large choice of non-linearities.