Special Session 3: Analysis of diffuse and sharp interface models

A Generalized Cahn-Hilliard equation with non-degenerate mobility: Well Posedness and Convergence to the Classical Cahn-Hilliard
Pietro Galimberti
University of Ferrara
Italy
Co-Author(s):    Monica Conti, Pietro Galimberti, Stefania Gatti and Andrea Giorgini
Abstract:
We study a generalized Cahn--Hilliard equation, based on an unconstrained theory proposed by Duda, Sarmiento and Fried in 2021, with non-degenerate mobility and nonlinear terms of logarithmic type. We prove well posedness of weak solutions, propagation of regularity and a type of separation from the pure states property for weak solutions, also in three space dimensions. Moreover, given that this model can be interpreted as a perturbation of the classical Cahn-Hilliard, we prove convergence of weak solutions to weak solutions of the Cahn-Hilliard equation on finite time intervals.