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Nonlocal-to-local convergence of the Cahn-Hilliard equation with degenerate mobility and the Flory-Huggins potential
Charles Elbar, Jakub Skrzeczkowski
The Cahn-Hilliard equation is a fundamental model for phase separation phenomena. Its rigorous derivation from the nonlocal aggregation equation, motivated by the desire to link in…
On the limit problem arising in the kinetic derivation of the Cahn-Hilliard equation
Charles Elbar, Benoît Perthame, Jakub Skrzeczkowski
The non-local degenerate Cahn-Hilliard equation is derived from the Vlasov equation with long-range attraction. We study the local limit as the delocalization parameter converges t…
Nonlocal Cahn-Hilliard equation with degenerate mobility: Incompressible limit and convergence to stationary states
Charles Elbar, Benoît Perthame, Andrea Poiatti +1
The link between compressible models of tissue growth and the Hele-Shaw free boundary problem of fluid mechanics has recently attracted a lot of attention. In most of these models,…
Degenerate Cahn-Hilliard systems: From nonlocal to local
José A. Carrillo, Charles Elbar, Jakub Skrzeczkowski
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…