Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations
The authors deal with reaction-diffusion systems including drift and modelling the transport of electrically charged species. In all previous studies a lower bound of the entropy dissipation in terms of the entropy were known, but in a nonconstructive way, that is, via a contradiction argument with no control on the constants. The goal of this paper is to provide quantitative exponential convergence to equilibrium with explicit rates and constants for reversible reaction processes of species \(A_i\), \(i= 1,2,\dots,q\), of the type \[ \alpha_1A_1+ \alpha_2A_2+\cdots+d_q A_q \rightleftarrows\beta_1A_1+\beta_2A_2+\cdots+\beta_qA_q,\;\alpha_i, \beta_i\in\mathbb{Z}_+ \] in a bounded box \(\Omega\subset \mathbb{R}^N\).
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