Validity of the weak diffusion expansion for solutions to systems of reaction-diffusion equations

Publisher Website
Google Scholar
Abstract
The regime of applicability of the weak diffusion expansion (WDE) for solutions to a generic system of reaction‐diffusion equations ∂ci/∂t = Di∇2ci + Qi(c) is delineated, where the enumerator index i runs 1 to n, ci = ci(x,t) denotes the concentration or density of the ith participating molecular or biological species, Di is the diffusivity constant for the ith species, and Qi(c) is an algebraic function of the n‐tuple c= (c1,⋅⋅⋅, cn) that expresses the local rate of production of the ith species due to chemical reactions or biological interactions. Our results take the form of rigorous upper bounds on the absolute value of the difference between the exact solution and the leading terms in the WDE for an approximate solution. It is shown by example that the leading terms in the WDE provide an approximate solution which can be very accurate for an appreciable duration of time.

This publication has 7 references indexed in Scilit: