The Caginalp phase-field system has been proposed in [4] as a simple mathematical model for phase transition phenomena. In this paper, we are concerned with a generalization of this system based on the Gurtin-Pipkin law with two temperatures for heat conduction with memory, apt to describe transition phenomena in nonsimple materials. The model consists of a parabolic equation governing the order parameter which is linearly coupled with a nonclassical integrodifferential equation ruling the evolution of the thermodynamic temperature of the material. Our aim is to construct a robust family of exponential attractors for the associated semigroup, showing the stability of the system with respect to the collapse of the memory kernel. We also study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.

On a Caginalp Phase-Field System with Two Temperatures and Memory / Conti, M.; Gatti, Stefania; Miranville, A.; Quintanilla,. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - 85:1(2017), pp. 1-27. [10.1007/s00032-017-0263-z]

On a Caginalp Phase-Field System with Two Temperatures and Memory

GATTI, Stefania;
2017

Abstract

The Caginalp phase-field system has been proposed in [4] as a simple mathematical model for phase transition phenomena. In this paper, we are concerned with a generalization of this system based on the Gurtin-Pipkin law with two temperatures for heat conduction with memory, apt to describe transition phenomena in nonsimple materials. The model consists of a parabolic equation governing the order parameter which is linearly coupled with a nonclassical integrodifferential equation ruling the evolution of the thermodynamic temperature of the material. Our aim is to construct a robust family of exponential attractors for the associated semigroup, showing the stability of the system with respect to the collapse of the memory kernel. We also study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.
2017
85
1
1
27
On a Caginalp Phase-Field System with Two Temperatures and Memory / Conti, M.; Gatti, Stefania; Miranville, A.; Quintanilla,. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - 85:1(2017), pp. 1-27. [10.1007/s00032-017-0263-z]
Conti, M.; Gatti, Stefania; Miranville, A.; Quintanilla,
File in questo prodotto:
File Dimensione Formato  
10.1007_s00032-017-0263-z(1).pdf

Accesso riservato

Descrizione: Articolo principale
Tipologia: Versione pubblicata dall'editore
Dimensione 1.39 MB
Formato Adobe PDF
1.39 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
VOR_On a Caginalp Phase-Field System with Two Temperatures and Memory.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 6.54 MB
Formato Adobe PDF
6.54 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
PRE_PRINT_CGMQ.pdf

Open access

Tipologia: Versione originale dell'autore proposta per la pubblicazione
Dimensione 404.35 kB
Formato Adobe PDF
404.35 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1136668
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact