Asymptotic behaviour of a conservative reaction-diffusion system associated with a Markov process algebra model

TL;DR

This paper studies the long-term behavior of conservative reaction-diffusion systems linked to Markov process algebra models, proving solutions converge to equilibrium and providing experimental validation.

Contribution

It introduces a lower and upper solution method to analyze asymptotic behavior of these systems, with a case study demonstrating convergence.

Findings

Solutions converge uniformly to equilibrium over time

Experimental results support theoretical convergence

Method applicable to Markovian process algebra models

Abstract

This paper demonstrates a lower and upper solution method to investigate the asymptotic behaviour of the conservative reaction-diffusion systems associated with Markovian process algebra models. In particular, we have proved the uniform convergence of the solution to its constant equilibrium for a case study as time tends to infinity, together with experimental results illustrations.