Global Existence for Reaction-Diffusion Systems Modeling Ions Electro-migration Through Biological Membranes with Mass Control and Critical Growth with Respect to the Gradient

Abstract

This paper studies the existence of global weak solutions for reaction-diffusion systems depending on two main assumptions: the non-negative of solutions and the total mass of components are preserved with time, the non-linearities have critical growth with respect to the gradient. This work is a generalization of the work developed by Alaa and Lefraich [2] without the presence of the gradient in the kinetic reaction terms.