On the existence and uniqueness of weak solutions of a coupled diffusion system related to image restoration

Abstract

In this study, the existence and uniqueness of the weak solution of a coupled diffusion system is presented. Since the considered problem is coupled and nonlinear, first we consider a corresponding linearized problem and then use a weak convergence method with Schauder fixed-point theorem to prove the existence of a weak solution of the underlying problem in an appropriate Hilbert space. Moreover, the computational experiments show that the considered model could be applied to image restoration problems.