A perturbation of the Cahn-Hilliard equation with logarithmic nonlinearity

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. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

The aim of this paper is to study a perturbation of the Cahn-Hilliard equation with nonlinear terms of logarithmic type. By proving the existence, regularity and uniqueness of solutions, as well as the (strong) separation properties of the solutions from the pure states, we finally demonstrate the convergence to the Cahn-Hilliard equation on finite time intervals.