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September  2006, 6(5): 1001-1026. doi: 10.3934/dcdsb.2006.6.1001

Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity

Elena Bonetti 1, , Pierluigi Colli 1, , Mauro Fabrizio 2, and  Gianni Gilardi 1,

1. 

Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy, Italy
2. 

Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy

Received  September 2005 Revised  November 2005 Published  June 2006

This paper deals with a thermomechanical model describing phase transitions with thermal memory in terms of balance and equilibrium equations for entropy and microforces, respectively. After a presentation and discussion of the model, the large time behaviour of the solutions to the related integro-differential system of PDE's is investigated.
Keywords: long-time behaviour of solutions., microforces, thermal memory, entropy, Phase transition model, non-linear initial-boundary value problem.
Mathematics Subject Classification: Primary: 35K60, 35Q99, 80A2.
Citation: Elena Bonetti, Pierluigi Colli, Mauro Fabrizio, Gianni Gilardi. Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1001-1026. doi: 10.3934/dcdsb.2006.6.1001
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