Validity of the weak diffusion expansion for solutions to systems of reactionhyphen;diffusion equations

摘要

The regime of applicability of the weak diffusion expansion (WDE) for solutions to a generic system of reactionhyphen;diffusion equations part;ci/part;t=Dinabla;2ci+Qi(c) is delineated, where the enumerator indexiruns 1 ton,ci=ci(x,t) denotes the concentration or density of theith participating molecular or biological species,Diis the diffusivity constant for theith species, andQi(c) is an algebraic function of thenhyphen;tuple c= (c1,sdot;sdot;sdot;,cn) that expresses the local rate of production of theith 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.