Improved convergence rates for the Hele-Shaw limit in the presence of confining potentials
Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to its applications to tissue growth and crowd motion modeling as it constitutes a way to link soft congestion (or compressible) models to hard congestion (or incompressible) descriptions. In this paper, we address the question of estimating the rate of this asymptotics in the presence of external drifts. In particular, we provide improved results in the 2-Wasserstein distance which are global in time thanks to the contractivity property that holds for strictly convex potentials.
Authors
- Filippo Santambrogio (ORCID: https://orcid.org/0000-0002-3333-1127)
- Noemi David
- Alpár R. Mészáros (ORCID: https://orcid.org/0000-0002-1824-376X)
Institutions
- Université Claude Bernard Lyon 1 (FR)
- Centre National de la Recherche Scientifique (FR)
- Durham University (GB)
- Institut Camille Jordan (FR)
- Laboratoire de Mathématiques Raphaël Salem (FR)
- Institut National des Sciences Appliquées de Lyon (FR)
Publication Details
- Journal
- Journal de l’École polytechnique — Mathématiques
- Published
- 2025-11-04
- DOI
- https://doi.org/10.5802/jep.322
- Citations
- 1
- Primary Topic
- Mathematical Biology Tumor Growth
- Type
- article
- Field-Weighted Citation Impact
- 1.37
Funders
- European Commission
- Durham University
- Agence Nationale de la Recherche
- King Abdullah University of Science and Technology
- Université de Lyon
- Engineering and Physical Sciences Research Council
- National Institute on Aging