A priori bounds for reaction–diffusion systems arising in chemical and biological dynamics

摘要

The authors investigate reaction–diffusion equations which arise in chemical and biological dynamics. It is shown that several common systems share a useful property, a structure on the non-linearity which arises from conservation of mass or population. This conservation property is used to demonstrate a priori bounds for the parabolic problems and the associated elliptic problem. The types of systems included in the analysis are the Gray–Scott system, SIR model, and the Selkov model of glycolysis.