The Penrose-Fife phase-field modelwith coupled dynamic boundary conditions

Alain Miranville; Elisabetta Rocca; Giulio Schimperna; Antonio Segatti

doi:10.3934/dcds.2014.34.4259

Article Contents

2014, Volume 34, Issue 10: 4259-4290. Doi: 10.3934/dcds.2014.34.4259

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The Penrose-Fife phase-field model with coupled dynamic boundary conditions

1.
Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex
2.
Dipartimento di Matematica, Università di Milano, Via Saldini, 50, I-20133 Milano
3.
Dipartimento di Matematica, Università di Pavia, Via Ferrata, 1, I-27100 Pavia
4.
Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, I-27100 Pavia

Received: December 31, 2012

Revised: March 31, 2013

Published: September 2014

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Abstract

In this paper we derive, starting from the basic principles of ther- modynamics, an extended version of the nonconserved Penrose-Fife phase tran- sition model, in which dynamic boundary conditions are considered in order to take into account interactions with walls. Moreover, we study the well- posedness and the asymptotic behavior of the initial-boundary value problem for the PDE system associated to the model, allowing the phase conguration of the material to be described by a singular function.

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Mathematics Subject Classification: 35K61, 35D30, 34B16, 74H40, 34K21, 80A22.

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