Generic reaction-diffusion model with application to image restoration and enhancement

Abstract

This article provides the existence of a global solution to a generic reaction-diffusion system. The main result is a generalization of the work presented by [2,5,11] in the case of a reaction-diffusion equation. We show the existence of a global weak solution to the considered system in the case of quasi-positivity and a triangular structure condition on the nonlinearities [12]. An example of application of our result is demonstrated on a novel bio-inspired image restoration model [1].

Keywords

• Reaction Diffusion
• image restoration
• parabolic system
• nonlinear partial differential equation
• Schauder fixed point