189 citations · 1.1k across the 48 of their papers we have counts for
52 papers
On time-splitting methods for gradient flows with two dissipation mechanisms
Alexander Mielke, Riccarda Rossi, Artur Stephan
We consider generalized gradient systems in Banach spaces whose evolutions are generated by the interplay between an energy functional and a dissipation potential. We focus on the…
An introduction to the analysis of gradients systems
Alexander Mielke
The present notes provide an extended version of a small lecture course given at the Humboldt Universität zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting…
A model of gravitational differentiation of compressible self-gravitating planets
Alexander Mielke, Tomas Roubicek, Ulisse Stefanelli
We present a dynamic model for inhomogeneous viscoelastic media at finite strains. The model features a Kelvin-Voigt rheology, and includes a self-generated gravitational field in…
Convergence to self-similar profiles in reaction-diffusion systems
Alexander Mielke, Stefanie Schindler
We study a reaction-diffusion system on the real line, where the reactions of the species are given by one reversible reaction according to the mass-action law. We describe differe…
Non-equilibrium steady states as saddle points and EDP-convergence for slow-fast gradient systems
Alexander Mielke
The theory of slow-fast gradient systems leads in a natural way to non-equilibrium steady states, because on the slow time scale the fast subsystem stays in steady states that are…
Self-Similar Pattern in Coupled Parabolic Systems as Non-Equilibrium Steady States
Alexander Mielke, Stefanie Schindler
We consider reaction-diffusion systems and other related dissipative systems on unbounded domains which would have a Liapunov function (and gradient structure) when posed on a fini…