Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions

Monica Conti; Stefania Gatti; Alain Miranville

doi:10.3934/dcdss.2012.5.485

Article Contents

2012, Volume 5, Issue 3: 485-505. Doi: 10.3934/dcdss.2012.5.485

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Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions

1.
Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano
2.
Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, I-41125 Modena
3.
Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 6086 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex

Received: April 30, 2011

Revised: June 30, 2011

Published: May 2012

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Abstract

This paper deals with the longtime behavior of the Caginalp phase-field system with coupled dynamic boundary conditions on both state variables. We prove that the system generates a dissipative semigroup in a suitable phase-space and possesses the finite-dimensional smooth global attractor and an exponential attractor.

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Mathematics Subject Classification: Primary: 35K55, 35J60; Secondary: 80A22.

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References

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