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On gradient flows and reaction-diffusion systems

  • Alexander Mielke (WIAS Berlin)
G3 10 (Lecture hall)

Abstract

Gradient system can be understood as mathematical realizations of the Onsager principle in thermodynamics, which states that the flux is given by a positive definite operator, called Onsager operator, times the thermodynamic driving force. We show that reaction-diffusion systems satisfying a detailed-balance condition can be formulated as a gradient system for the relative entropy and an Onsager operator (inverse of the Riemannian tensor), which is given as a sum of a diffusion part (Wasserstein metric) and a reaction part. This approach allows us to connect gradient-flow formulations of discrete many-particle systems with their continuous limits. Moreover, well-established concepts for scalar equations, as geodesic lambda-convexity or exponential decay into equilibrium, can be generalized to these more general systems.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail

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