Asymptotic behavior of a Cahn-Hilliard/Allen-Cahn system with temperature

Alain Miranville; Ramon Quintanilla; Wafa Saoud

doi:10.3934/cpaa.2020099

Article Contents

2020, Volume 19, Issue 4: 2257-2288. Doi: 10.3934/cpaa.2020099

This issue Previous Article Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations Next Article The stampacchia maximum principle for stochastic partial differential equations forced by lévy noise

Asymptotic behavior of a Cahn-Hilliard/Allen-Cahn system with temperature

1.
Université de Poitiers, , Laboratoire de Mathématiques et Applications, UMR CNRS 7348, SP2MI, , Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France
2.
E.S.E.I.A.A.T. -U.P.C, Departament de Matemátiques, Colom 11, 08222 Terrassa, Barcelona, Spain
3.
The International University of Beirut, Department of Mathematics and Physics, Tal Abbas Road, Halba-Akkar, Lebanon

Dedicated to Professor Tomás Caraballo on occasion of his sixtieth birthday

Received: October 31, 2018

Revised: August 31, 2019

Published: January 2020

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Abstract

The main goal of this paper is to study the asymptotic behavior of a coupled Cahn-Hilliard/Allen-Cahn system with temperature. The work is divided into two parts: In the first part, the heat equation is based on the usual Fourier law. In the second one, it is based on the type Ⅲ heat conduction law. In both parts, we prove the existence of exponential attractors and, therefore, of finite-dimensional global attractors.

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Mathematics Subject Classification: 35B40, 35B41, 35B45, 35K05, 35K51.

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