CC BY 4.0 UnportedStephan, Artur2022-03-222022-03-222021https://oa.tib.eu/renate/handle/123456789/8315https://doi.org/10.34657/7353We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We understand the linear reaction-diffusion system 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 structure 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 diffusion equation with a mixed diffusion constant for the coarse-grained slow variable. © 2021, The Author(s).enghttps://creativecommons.org/licenses/by/4.0/510geometric structureWasserstein metriclinear reaction-diffusion systemEDP-convergenceArticle