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

• Main Authors: Amal Aarab, Nour Eddine Alaa, Hamza Khalfi
• Format: Article
• Language: English
• Published: Texas State University 2018-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: Reaction Diffusion; image restoration; parabolic system; nonlinear partial differential equation; Schauder fixed point
• Online Access: http://ejde.math.txstate.edu/Volumes/2018/125/abstr.html

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].