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.
Degenerate Cahn-Hilliard systems: From nonlocal to local
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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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Nonlocal approximation of an anisotropic cross-diffusion system
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.