On the equilibriation of chemical reaction-diffusion systems with degenerate reactions

TL;DR

This paper proves the convergence to equilibrium for reaction-diffusion systems with degenerate reactions and nonlinearities of arbitrary order, using entropy methods and functional inequalities, even when diffusion and reactions are confined to subsets of the domain.

Contribution

It introduces a novel approach to establish convergence to equilibrium in complex reaction-diffusion systems with degenerate processes and arbitrary nonlinearities.

Findings

Proves convergence to equilibrium using entropy methods.

Handles nonlinearities of arbitrary order.

Addresses degenerate diffusion and reactions on subsets of the domain.

Abstract

The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing functional inequalities in terms of entropy method. Our approach allows us to deal with nonlinearities of arbitrary orders, for which only global renormalised solutions are known to globally exist. For bounded solutions, we also prove the convergence to equilibrium when the diffusion as well as the reaction are degenerate, that is both diffusion and reaction processes only act on specific subsets of the domain.