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1997 Well-posedness of the weak formulation for the phase-field model with memory
Pierluigi Colli, Gianni Gilardi, Maurizio Grasselli
Adv. Differential Equations 2(3): 487-508 (1997).


A phase-field model based on the Gurtin-Pipkin heat flux law is considered. This model consists in a Volterra integrodifferential equation of hyperbolic type coupled with a nonlinear parabolic equation. The system is then associated with a set of initial and Neumann boundary conditions. The resulting problem was already studied by the authors who proved existence and uniqueness of a smooth solution. A~careful and detailed investigation on weak solutions is the goal of this paper, going from the aspects of the approximation to the proof of continuous dependence estimates. In addition, a sufficient condition for the boundedness of the phase variable is given.


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Pierluigi Colli. Gianni Gilardi. Maurizio Grasselli. "Well-posedness of the weak formulation for the phase-field model with memory." Adv. Differential Equations 2 (3) 487 - 508, 1997.


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

zbMATH: 1023.45501
MathSciNet: MR1441853

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

Rights: Copyright © 1997 Khayyam Publishing, Inc.


Vol.2 • No. 3 • 1997
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