Generic reaction-diffusion model with application to image restoration and enhancement

Date

2018-06-18

Authors

Aarab, Amal
Alaa, Nour Eddine
Khalfi, Hamza

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

This article provides the existence of a global solution to a generic reaction-diffusion system. The main result is a generalization of the work presented by [2,5,11] in the case of a reaction-diffusion equation. We show the existence of a global weak solution to the considered system in the case of quasi-positivity and a triangular structure condition on the nonlinearities [12]. An example of application of our result is demonstrated on a novel bio-inspired image restoration model [1].

Description

Keywords

Reaction Diffusion, Image restoration, Parabolic system, Nonlinear partial differential equation, Schauder fixed point

Citation

Aarab, A., Alaa, N. E., & Khalfi, H. (2018). Generic reaction-diffusion model with application to image restoration and enhancement. <i>Electronic Journal of Differential Equations, 2018</i>(125), pp. 1-12.

Rights

Attribution 4.0 International

Rights Holder

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights License