Mathematical analysis of a modified Weikert system for image enhancement

Abstract

This paper tackles the problem of proving global existence for an abstract nonlinear Reaction-Diffusion system inspired by the famous Weickert model. We show the existence of a global weak solution to a truncated version of the proposed system using a fixed point approach. Then, we establish some crucial estimates under Quasi-positivity and a Triangular Structure condition on the nonlinearities. On passage to the limit, we recover the original system and prove the existence for only integrable nonlinearities and initial conditions.