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

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.