Theoretical Analysis Of A Nonlinear Parabolic System Derived From The Color Image Denoising

This thesis will propose a nonlinear partial differential equation model for the color image denoising and reconstruction, and mainly study the well-posedness for the associated initial-boundary value problem. First, for the color image processing we consider the usual CB model, where C and B represent the chromaticity and brightness of the image respectively. Then, to deal with the chromaticity and brightness separately we propose two models of nonlinear partial differential equations. The main part of this thesis is to establish the existence, uniqueness and stability of weak solutions to the initial-boundary value problem of an associated nonlinear parabolic system with nonlocal terms by using energy estimates and the Schauder fixed point theorem.