Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

On nonlinear cross-diffusion systems: an optimal transport approach

Abstract : We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of discrete-time solutions. Its continuum limit, due to the possible mixing of the densities, only solves a weaker version of the original system. In one space dimension, where the densities are guaranteed to be segregated, a stable interface appears between the two densities, and a stronger convergence result, in particular derivation of a standard weak solution to the system, is available. We also study the incompressible limit of the system, which addresses transport under a height constraint on the total density. In one space dimension we show that the problem leads to a two-phase Hele-Shaw type flow.
Document type :
Preprints, Working Papers, ...
Complete list of metadata
Contributor : Alpár Richárd Mészáros Connect in order to contact the contributor
Submitted on : Friday, August 18, 2017 - 4:26:21 PM
Last modification on : Wednesday, August 7, 2019 - 12:14:40 PM

Links full text


  • HAL Id : hal-01575286, version 1
  • ARXIV : 1705.02457



Inwon Kim, Alpár R. Mészáros. On nonlinear cross-diffusion systems: an optimal transport approach. 2017. ⟨hal-01575286⟩



Record views