On the hyperbolic relaxation of the Cahn–Hilliard equation with a mass source

Article type: Research Article

Authors: Dor, Dieunel^{a; b; *}

Affiliations: [a] Laboratoire de Mathematiques et Applications, Universite de Poitiers, UMR CNRS 7348, SP2MI, Boulevard Marie et Pierre Curie-Teleport 2 F-86962 Chasseneuil Futuroscope Cedex, France | [b] Ecole Normale Superieure, Laboratoire de Mathematiques et Applications (LAMA-UEH), Universite d’Etat d’Haiti, HT6115, 2 Rue Caseus, Pacot, Port-au-Prince, Haiti

Correspondence: [*] Corresponding author. E-mail: dordieunel97@gmail.com.

Abstract: In this paper, we consider the hyperbolic Cahn–Hilliard equation with a proliferation term, which has applications in biology. First, we study the well-posedness and the regularity of the solutions, which then allow us to study the dissipativity and the high-order dissipativity and finally the existence of the exponential attractor with Dirichlet boundary conditions. Finally, we give numerical simulations that confirm the results.

Keywords: Cahn-Hilliard equation, relaxation term, mass source, well posedness, tumor growth, global attractor, exponential attractor, simulations

DOI: 10.3233/ASY-231844

Journal: Asymptotic Analysis, vol. 135, no. 1-2, pp. 25-53, 2023