Existence of solution to a Cahn–Hilliard equation

Article type: Research Article

Authors: Mourad, Ayman^a | Taha, Zahraa^{b; c; *}

Affiliations: [a] Department of Mathematics, Faculty of Sciences (I), Lebanese University, Beirut, Lebanon | [b] Laboratoire de Mathématiques et Applications, UMR CNRS 7348, Université de Poitiers, TSA 61125, 11 Boulevard Marie et Pierre Curie, 86073 Poitiers Cedex 9, France | [c] Mathematics Laboratory, Doctoral School of Sciences and Technology, Lebanese University, Beirut, Lebanon

Correspondence: [*] Corresponding author. E-mail: taha.zahraa@math.univ-poitiers.fr.

Abstract: Our aim in this paper is to prove the existence to a Cahn–Hilliard equation with a proliferation term and endowed with Neumann boundary conditions. Such a model has, in particular, applications in biology. We first consider regular nonlinear term then logarithmic one. We finally give some numerical simulations which confirm the theoretical results.

Keywords: Cahn-Hilliard equation, proliferation term, regular nonlinear term, logarithmic nonlinear term, existence, simulations

DOI: 10.3233/ASY-221756

Journal: Asymptotic Analysis, vol. 130, no. 3-4, pp. 387-408, 2022