Pullback attractor for a nonautonomous parabolic Cahn-Hilliard phase-field system

Jean De Dieu Mangoubi; Mayeul Evrard Isseret Goyaud; Daniel Moukoko; Jean De Dieu Mangoubi; Mayeul Evrard Isseret Goyaud; Daniel Moukoko

doi:10.3934/math.20231123

AIMS Mathematics

2023, Volume 8, Issue 9: 22037-22066. doi: 10.3934/math.20231123

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Research article

Pullback attractor for a nonautonomous parabolic Cahn-Hilliard phase-field system

Faculté des Sciences et Technique, Université Marien Ngouabi, BP: 69, Brazzaville, Congo

Received: 08 April 2023 Revised: 27 June 2023 Accepted: 27 June 2023 Published: 12 July 2023
MSC : 35B41, 35B45, 35K55

Our aim in this paper is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory involving two temperatures and a nonlinear coupling. In particular, we prove well-posedness results. More precisely, the existence of a pullback attractor for a nonautonomous parabolic of type Cahn-Hilliard phase-field system. The pullback attractor is a compact set, invariant with respect to the cocycle and which attracts the solutions in the neighborhood of minus infinity, consequently the attractor pullback (or attractor retrograde) exhibits a infinite fractal dimension.
- attractor,
- pullback $ \omega $-limit compact,
- pullback condition,
- norm-to-weak continuous,
- nonautonomous parabolic Cahn-Hilliard phase-field system
Citation: Jean De Dieu Mangoubi, Mayeul Evrard Isseret Goyaud, Daniel Moukoko. Pullback attractor for a nonautonomous parabolic Cahn-Hilliard phase-field system[J]. AIMS Mathematics, 2023, 8(9): 22037-22066. doi: 10.3934/math.20231123

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Abstract

Our aim in this paper is to study generalizations of the Caginalp phase-field system based on a thermomechanical theory involving two temperatures and a nonlinear coupling. In particular, we prove well-posedness results. More precisely, the existence of a pullback attractor for a nonautonomous parabolic of type Cahn-Hilliard phase-field system. The pullback attractor is a compact set, invariant with respect to the cocycle and which attracts the solutions in the neighborhood of minus infinity, consequently the attractor pullback (or attractor retrograde) exhibits a infinite fractal dimension.

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