77 citations · 311 across the 32 of their papers we have counts for
35 papers
Nonlinear Diffusion Equations: Full characterization of Entropies
Anton Arnold, Jose A. Carrillo, Daniel Matthes
This paper is concerned with the large-time behavior of quasilinear Fokker-Planck equations with confinement on the whole space . It aims at characterizing all relati…
Covariance-modulated optimal transport and gradient flows
Martin Burger, Matthias Erbar, Franca Hoffmann +2
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics…
Entropic transfer operators
Oliver Junge, Daniel Matthes, Bernhard Schmitzer
We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized opt…
Exponential convergence to equilibrium for coupled systems of nonlinear degenerate drift diffusion equations
Lisa Beck, Daniel Matthes, Martina Zizza
We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein dist…
Gradient Flow Structure of a Multidimensional Nonlinear Sixth Order Quantum-Diffusion Equation
Daniel Matthes, Eva-Maria Rott
A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction of a model from quantum statistical mechanics, and also as the gradient flow of a seco…
Construction of a two-phase flow with singular energy by gradient flow methods
Clément Cancès, Daniel Matthes
We prove the existence of weak solutions to a system of two diffusion equations that are coupled by a pointwise volume constraint. The time evolution is given by gradient dynamics…