Advances in Differential Equations

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

Pierluigi Colli, Gianni Gilardi, and Maurizio Grasselli

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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

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

First available in Project Euclid: 23 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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