A singular cahn-hilliard-oono phase-field system with hereditary memory

Monica Conti; Stefania Gatti; Alain Miranville

doi:10.3934/dcds.2018132

Article Contents

2018, Volume 38, Issue 6: 3033-3054. Doi: 10.3934/dcds.2018132

This issue Previous Article High energy solutions of the Choquard equation Next Article Interface stabilization of a parabolic-hyperbolic pde system with delay in the interaction

A singular cahn-hilliard-oono phase-field system with hereditary memory

1.
Politecnico di Milano, Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, I-20133 Milano, Italy
2.
Università di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Via Campi 213/B, I-41125 Modena, Italy
3.
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
4.
Xiamen University, School of Mathematical Sciences, 361005 Xiamen, Fujian, China

* Corresponding author: Stefania Gatti
* Corresponding author: Stefania Gatti

Received: August 31, 2017

Published: May 2018

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Abstract

We consider a phase-field system modeling phase transition phenomena, where the Cahn-Hilliard-Oono equation for the order parameter is coupled with the Coleman-Gurtin heat law for the temperature. The former suitably describes both local and nonlocal (long-ranged) interactions in the material undergoing phase-separation, while the latter takes into account thermal memory effects. We study the well-posedness and longtime behavior of the corresponding dynamical system in the history space setting, for a class of physically relevant and singular potentials. Besides, we investigate the regularization properties of the solutions and, for sufficiently smooth data, we establish the strict separation property from the pure phases.

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Mathematics Subject Classification: Primary: 35B41, 35K55, 35L05, 80A22.

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