Our aim in this paper is to study a perturbation of the Cahn–Hilliard equation with nonlinear terms of logarithmic type. This new model is based on an unconstrained theory recently proposed in [5]. We prove the existence, regularity and uniqueness of solutions, as well as (strong) separation properties of the solutions from the pure states, also in three space dimensions. We finally prove the convergence to the Cahn–Hilliard equation, on finite time intervals.
A perturbation of the Cahn–Hilliard equation with logarithmic nonlinearity / Conti, Monica; Gatti, Stefania; Miranville, Alain. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 382:(2024), pp. 50-76. [10.1016/j.jde.2023.11.013]
A perturbation of the Cahn–Hilliard equation with logarithmic nonlinearity
Conti, Monica;Gatti, Stefania;Miranville, Alain
2024
Abstract
Our aim in this paper is to study a perturbation of the Cahn–Hilliard equation with nonlinear terms of logarithmic type. This new model is based on an unconstrained theory recently proposed in [5]. We prove the existence, regularity and uniqueness of solutions, as well as (strong) separation properties of the solutions from the pure states, also in three space dimensions. We finally prove the convergence to the Cahn–Hilliard equation, on finite time intervals.
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