Global existence and asymptotic behavior for a reaction-diffusion system with unbounded coefficients

TL;DR

This paper studies a reaction-diffusion system with unbounded coefficients, proving exponential decay of solutions using analytic semigroup properties, relevant for modeling catalytic chemical reactions.

Contribution

It introduces a novel analysis of reaction-diffusion systems with unbounded, time-dependent coefficients, establishing exponential decay of solutions.

Findings

Proved exponential decay of solutions.

Analyzed systems with unbounded, time-dependent coefficients.

Applied properties of analytic semigroups.

Abstract

We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different polynomial reaction terms. An exponential decay of the globally bounded solutions is proved. The key tool of the proofs are properties of analytic semigroups and some inequalities.