title: Gradient structures and geodesic convexity for reaction-diffusion systems.
abstract: We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic λ-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion system, provide a survey on the applicability of the theory.
authors.affiliation: Weierstraß-Institut für Angewandte Analysis und Stochastik, , Mohrenstraße 39, 10117 Berlin, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Liero
authors.forename: Alexander
authors.initials: A
authors.lastname: Mielke
keywords: Onsager operator; Wasserstein metric; geodesic convexity; gradient structures; reaction–diffusion system; relative entropy