Simple proofs for the existence of smooth solutions to a reaction-diffusion system modeling reversible chemistry

Abstract

We present in this work a very short proof for the existence, uniqueness and smoothness in dimensions $d\le 3$ of the system of reaction diffusion $\partial \_ta\_i-d\_i\Delta a\_i=(-1{)}^i(a\_1a\_3-a\_2a\_4)$, where $a\_i\ge 0$ model the concentrations of chemical species undergoing a chemical reaction and diffusing (each with its diffusion rate $d\_i>0$) in a bounded container.