Mathematical analysis of a reaction diffusion model for image restoration

Abstract

In this paper, we propose a modification and a generalization of
the theory developed by P. Perona and J. Malik for edge detection and image restoration, from the case of a single equation to the case of nonlinear reaction-diffusion system. We are interested in the existence of weak solutions for this system for which two main properties hold: the positivity of the solutions and the total mass of the components are preserved with time.