5 papers · 1 filter
The Aronson-Bénilan estimate for a Lagrangian particle discretization of the Porous Medium Equation
Marco Di Francesco, Daniel Matthes
We consider a nearest neighbor, Lagrangian particle discretization of the one dimensional porous medium equation. We prove that the particle model satisfies a discrete analog of th…
The spatially discrete to continuous limit in the nonlocal quantum diffusion equation
Daniel Matthes, Eva-Maria Rott
We propose and analyse a spatial discretization of the non-local Quantum Drift Diffusion (nlQDD) model by Degond, Mèhats and Ringhofer in one space dimension. With our approach, t…
A structure preserving discretization for the Derrida-Lebowitz-Speer-Spohn equation based on diffusive transport
Daniel Matthes, Eva-Maria Rott, Giuseppe Savaré +1
We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the circle. Our choice of discretization is motivated by a novel gradient flow formulation with r…
Diffusive transport on the real line: semi-contractive gradient flows and their discretization
Daniel Matthes, Eva-Maria Rott, André Schlichting
The diffusive transport distance, a novel pseudo-metric between probability measures on the real line, is introduced. It generalizes Martingale optimal transport, and forms a hiera…
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…