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Continuum of coupled Wasserstein gradient flows
Clément Cancès, Daniel Matthes, Ismael Medina +1
We study a system of drift-diffusion PDEs for a potentially infinite number of incompressible phases, subject to a joint pointwise volume constraint. Our analysis is based on the i…
Convergence to equilibrium for cross diffusion systems with nonlocal interaction
Daniel Matthes, Christian Parsch
We study the existence and the rate of equilibration of weak solutions to a two-component system of non-linear diffusion-aggregation equations, with small cross diffusion effects.…
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…
Existence of solutions for a class of fourth order cross-diffusion systems of gradient flow type
Daniel Matthes, Jonathan Zinsl
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow…