We have created a functional framework for a class of non-metric gradient systems. The
state space is a space of nonnegative measures, and the class of systems includes the …

We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type.
We show how such dissipation potentials emerge in large deviations of jump processes …

We study a class of nonlocal partial differential equations presenting a tensor-mobility, in
space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our …

The present notes provide an extended version of a small lecture course given at the
Humboldt Universit\" at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material …

We consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast
reactions. It is known that the fast-reaction-rate limit can be described by an ODE with …

We consider linear reaction systems with slow and fast reactions, which can be interpreted
as master equations or Kolmogorov forward equations for Markov processes on a finite state …

For gradient systems depending on a microstructure, it is desirable to derive a macroscopic
gradient structure describing the effective behavior of the microscopic scale on the …

We study asymptotic limits of reversible random walks on tessellations via a variational
approach which relies on a specific generalized gradient flow formulation of the …

We consider finite-volume approximations of Fokker--Planck equations on bounded convex
domains in R^d and study the corresponding gradient flow structures. We reprove the …

Abstract The notion of Energy-Dissipation-Principle convergence (EDP-convergence) is
used to derive effective evolution equations for gradient systems describing diffusion in a …