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,
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1136668
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