Coarse‐graining via EDP‐convergence for linear fast‐slow reaction‐diffusion systems

Abstract

AbstractIn [7] a fast‐reaction limit for a linear reaction‐diffusion system consisting of two diffusion equations coupled by a linear reaction is performed. The linear reaction‐diffusion system is understood as a gradient flow of the free energy in the space of probability measures equipped with a geometric structure, which contains the Wasserstein metric for the diffusion part and cosh‐type functions for the reaction part. The fast‐reaction limit is done on the level of the gradient system by proving EDP‐convergence with tilting. The limit gradient system induces a diffusion system with Lagrange multipliers on the linear slow‐manifold. Moreover, the limit gradient system can be equivalently described by a coarse‐grained gradient system, which induces a scalar diffusion equation with a mixed diffusion constant for the coarse‐grained slow variable.