Global existence for reaction-diffusion systems modeling ions electro-migration through biological membranes with mass control and critical growth with respect to the gradient

Bassam Al-hamzah, Naji Yebari


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 \cite{1} without the presence of the gradient in the kinetic reaction terms.


Global solutions; nonlinear parabolic; reaction-diffusion systems; Schauders fixed point

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