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Research Article | Open Access

On the modified of the one-dimensional Cahn-Hilliard equation with a source term

Universite de Poitiers, Laboratoire de Mathematiques et Applications, UMR CNRS 7348, SP2MI, Boulevard Marie et Pierre Curie-Teleport 2 F-86962 Chasseneuil Futuroscope Cedex, France
Departement de Mathematiques, Universite d'Etat d'Haiti, Ecole Normale Superieure, Laboratoire des Sciences pour l'Environnement et l'Energie (LS2E), HT6115 Canape-Vert, Port-au-Prince, Haiti
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Abstract

We consider the modified Cahn-Hilliard equation that govern the relative concentration ϕ of one component of a binary system. This equation is characterized by the presence of the additional inertial term τ D d 2 ϕ d t 2 which stands for the relaxation of the diffusion flux. This equation is associated with Dirichlet boundary conditions. We study the existence, uniqueness and regularity of solutions in one space dimension. We also prove the existence of the global attractor and exponential attractors.

Keywords

Cahn-Hilliard equationwell posednessstrongly continous semigroupsgloball attractorsrobust exponential attractors
CLC number: 35G20, 35L60, 35Q92, 35B41

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 14672-14695
DOI: 10.3934/math.2022807

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DOR D. On the modified of the one-dimensional Cahn-Hilliard equation with a source term. AIMS Mathematics, 2022, 7(8): 14672-14695. https://doi.org/10.3934/math.2022807

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Received: 03 January 2022
Revised: 21 March 2022
Accepted: 19 April 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)