THE GLOBAL EXISTENCE OF SOLUTIONS TO REACTION-DIFFUSION SYSTEM
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Date
2026
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Abstract
The purpose of this work is to study the global existence of solutions for reaction-diffusion
systems. We construct suitable Lyapunov functionals based on the solutions of the coupled
reaction-diffusion equations in order to derive (Lp) bounds for the solutions. When the reaction
terms are sufficiently regular, using the well known regularizing eect, we deduce the existence of
global solutions.
The first part of this work is devoted to reaction-diffusion systems with diagonal diffusion
matrices, where global existence results are obtained under appropriate assumptions on the re
action terms. In the second part, the analysis is extended to systems with full diffusion matrices,
where we prove the existence of global solutions for a coupled 2-component reaction-diffusion
system with a full matrix diffusion. We show that some results of global and bounded solutions
are established via invariant regions and the Lyapunov functional.