On the Cahn–Hilliard–Forest equations with logarithmic nonlinear terms

Our aim in this paper is to study the regularity of solutions to a variant of the Cahn–Hilliard equation with logarithmic nonlinear terms. This model was proposed by S. Forest and is based on microconcentrations. It has applications to Lithium-Ion batteries and is efficient in numerical simulations. Furthermore, we are able to prove the strict separation from the pure states in one space dimension; note that, as far as the original Cahn–Hilliard equation is concerned, this property is known in one and two space dimensions.