## Topological Methods in Nonlinear Analysis

### 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 53, Number 1 (2019), 225-256.

Dates
First available in Project Euclid: 20 February 2019

https://projecteuclid.org/euclid.tmna/1550631834

Digital Object Identifier
doi:10.12775/TMNA.2018.045

Mathematical Reviews number (MathSciNet)
MR3939154

Zentralblatt MATH identifier
07068335

#### Citation

Al-Hamzah, Bassam; Yebari, Naji. Global Existence for Reaction-Diffusion Systems Modeling Ions Electro-migration Through Biological Membranes with Mass Control and Critical Growth with Respect to the Gradient. Topol. Methods Nonlinear Anal. 53 (2019), no. 1, 225--256. doi:10.12775/TMNA.2018.045. https://projecteuclid.org/euclid.tmna/1550631834

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