Mathematical Analysis of a Degenerate Reaction-Diffusion Model

Abstract

In this paper, we are interested in the study of a degenerate reaction-diffusion model, where we prove the existence of positive maximal and minimal solutions, including the uniqueness of the positive solution. The technique used is mainly based on the method of upper and lower solutions.

Generalized result on the global existence of positive solutions for a parabolic reaction diffusion model with a full diffusion matrix

“…In the works of Mesbahi and Alaa [1], [2], [17] and [18], we find new developed methods based on truncation functions, fixed point theorems and compactness, etc.…”

On the existence of positive solutions of a class of parabolic reaction di usion systems

“…For the mathematical analysis of this type of problem, various methods and elaborate techniques have been proposed, see for example Mesbahi et al [1], [2], [16], [15], Gontara [9], Lions [10], Maâgli et al [13], [12], Pierre [17] and Zhang [20], [19]. We refer the reader to Arakelian and Gauthier [3], Armitage and Gardiner [4] and Port [18] for more details on the potential arguments of the theory that interest us mainly in this work.…”