Advances in Differential Equations

Global smooth solution to the standard phase-field model with memory

Pierluigi Colli, Gianni Gilardi, and Maurizio Grasselli

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Adv. Differential Equations Volume 2, Number 3 (1997), 453-486.

Dates
First available in Project Euclid: 23 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366742252

Mathematical Reviews number (MathSciNet)
MR1441852

Zentralblatt MATH identifier
1023.45500

Subjects
Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
Secondary: 35K55: Nonlinear parabolic equations 73B30 80A20: Heat and mass transfer, heat flow

Citation

Colli, Pierluigi; Gilardi, Gianni; Grasselli, Maurizio. Global smooth solution to the standard phase-field model with memory. Adv. Differential Equations 2 (1997), no. 3, 453--486. https://projecteuclid.org/euclid.ade/1366742252.


Export citation