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1997 Global smooth solution to the standard phase-field model with memory
Pierluigi Colli, Gianni Gilardi, Maurizio Grasselli
Adv. Differential Equations 2(3): 453-486 (1997).

Abstract

This paper is devoted to study the so-called phase-field model when the classical Fourier law is replaced by the Gurtin-Pipkin constitutive assumption. The resulting system of partial differential equations is investigated in a quite general setting. A hyperbolic equation is coupled with a parabolic variational inequality, the state variables being temperature and non-conserved order parameter. By including initial and boundary conditions, the existence and uniqueness of strong solutions is shown along with regularity results ensuring the global boundedness of both the unknowns.

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Pierluigi Colli. Gianni Gilardi. Maurizio Grasselli. "Global smooth solution to the standard phase-field model with memory." Adv. Differential Equations 2 (3) 453 - 486, 1997.

Information

Published: 1997
First available in Project Euclid: 23 April 2013

zbMATH: 1023.45500
MathSciNet: MR1441852

Subjects:
Primary: 45K05
Secondary: 35K55, 73B30, 80A20

Rights: Copyright © 1997 Khayyam Publishing, Inc.

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Vol.2 • No. 3 • 1997
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