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Journal Articles Journal of Differential Equations Year : 2023

Degenerate Cahn-Hilliard equation: From nonlocal to local

Abstract

There has been recently an important interest in deriving rigorously the Cahn-Hilliard equation from the nonlocal equation, also called aggregation equation. So far, only non-degenerate mobilities were treated. Since we are motivated by models for the biomechanics of living tissues, it is useful to include degenerate motilities. In this framework, we present a new method to show the convergence of the nonlocal to the local degenerate Cahn-Hilliard equation. The method includes the use of nonlocal Poincar\'e and compactness inequalities.

Dates and versions

hal-04043519 , version 1 (23-03-2023)

Identifiers

Cite

Charles Elbar, Jakub Skrzeczkowski. Degenerate Cahn-Hilliard equation: From nonlocal to local. Journal of Differential Equations, 2023, 364, pp.576-611. ⟨10.1016/j.jde.2023.03.057⟩. ⟨hal-04043519⟩
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