Long time convergence for a classof variational phase-field models

Pierluigi Colli; Danielle Hilhorst; Françoise Issard-Roch; Giulio Schimperna

doi:10.3934/dcds.2009.25.63

Article Contents

2009, Volume 25, Issue 1: 63-81. Doi: 10.3934/dcds.2009.25.63

This issue Previous Article Symmetries of evolution equations with non-local operators and applications to the Boltzmann equation Next Article Over-populated tails for conservative-in-the-mean inelastic Maxwell models

Long time convergence for a class of variational phase-field models

1.
Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, I-27100 Pavia
2.
CNRS and Laboratoire de Mathématiques, Université Paris-Sud 11, Bat. 425, F-91405 Orsay
3.
Dipartimento di Matematica "F.Casorati", Università di Pavia, Via Ferrata, 1, I-27100 Pavia

Received: November 30, 2007

Published: December 2008

Abstract Related Papers Cited by

Abstract

In this paper we analyze a class of phase field models for the dynamics of phase transitions which extend the well-known Caginalp and Penrose-Fife phase field models. We prove the existence and uniqueness of the solution of a corresponding initial boundary value problem and deduce further regularity of the solution by exploiting the so-called regularizing effect. Finally we study the long time behavior of the solution and show that it converges algebraically fast to a stationary solution as $t$ tends to infinity.

Keywords:

Mathematics Subject Classification: Primary: 35B40, 35K45; Secondary: 80A22.

Citation:

Article Metrics

HTML views() PDF downloads(57) Cited by(0)

Long time convergence for a class of variational phase-field models

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Long time convergence for a class of variational phase-field models

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content