Degenerate Cahn-Hilliard systems: From nonlocal to local

2023/03/21 by José A. Carrillo, Charles Elbar, Carrillo, José A. +3 · 1 citation
Computer Science · Mathematics · Materials Science · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2303.11929

Abstract

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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