A Weak Comparison Principle for Reaction-Diffusion Systems

Abstract EN

We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions.

We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay.

Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.