GLOBAL EXISTENCE IN REACTION DIFFUSION NONLINEAR PARABOLIC PARTAIL DIFFERENTIAL EQUATION IN IMAGE PROCESSING

Abstract

This paper deals with the equation. We give the proof of global existence of our nonlinear reaction diffusion of problem (P). In the first we define an approximating scheme and by using Schauder fixed point theorem in ordered Banach spaces, we show the existence of a solution for this approached problem. Finally by making some estimations we prove that the solution of the truncated equation converge to the solution of our problem. We use a new technique recently introduced in order to generalize some of interesting prior works that has been presented.