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Degenerate Cahn-Hilliard systems: From nonlocal to local

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arxiv 2303.11929 v1 pith:J7FLHESQ submitted 2023-03-21 math.AP

José A. Carrillo , Charles Elbar , Jakub Skrzeczkowski This is my paper · ORCID
classification math.AP
keywords systemcahn-hilliarddegeneratelocalmodelnonlocaladhesionanalysis
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We provide a rigorous mathematical framework to establish the limit of a nonlocal model of cell-cell adhesion system to a local model. When the parameter of the nonlocality goes to 0, the system tends to a Cahn-Hilliard system with degenerate mobility and cross interaction forces. Our analysis relies on a priori estimates and compactness properties.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonlocal approximation of an anisotropic cross-diffusion system

    math.AP 2024-12 conditional novelty 6.0 of 10

    Weak solutions of an anisotropic nonlocal cross-diffusion system converge to weak solutions of the corresponding local cross-diffusion system in the vanishing viscosity limit.

  2. A nonlocal-to-local approach to aggregation-diffusion equations

    q-bio.CB 2025-05 conditional novelty 2.0 of 10

    A short-range limit of nonlocal aggregation-diffusion equations yields a local thin-film-type model whose four parameters can be tuned to reproduce sorting, engulfment, partial engulfment, and mixing of two cell populations.

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