3 papers
math.AP2025
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…
math.AP2025
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…
math.AP2025
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…