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2008 On a doubly nonlinear phase-field model for first-order transitions with memory
V. Berti, M. Fabrizio, C. Giorgi
Differential Integral Equations 21(3-4): 325-350 (2008). DOI: 10.57262/die/1356038783


Solid-liquid transitions in thermal insulators and weakly conducting media are modeled through a phase-field system with memory. The evolution of the phase variable ${\varphi}$ is ruled by a balance law which takes the form of a Ginzburg-Landau equation. A thermodynamic approach is developed starting from a special form of the internal energy and a nonlinear hereditary heat conduction flow of Coleman-Gurtin type. After some approximation of the energy balance, the absolute temperature ${\theta}$ obeys a doubly nonlinear ``heat equation" where a third-order nonlinearity in ${\varphi}$ appears in place of the (customarily constant) latent-heat. The related initial and boundary value problem is then formulated in a suitable setting and its well--posedness and stability is proved.


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V. Berti. M. Fabrizio. C. Giorgi. "On a doubly nonlinear phase-field model for first-order transitions with memory." Differential Integral Equations 21 (3-4) 325 - 350, 2008.


Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35029
MathSciNet: MR2484012
Digital Object Identifier: 10.57262/die/1356038783

Primary: 35G30
Secondary: 35B30 , 45K05 , 80A22

Rights: Copyright © 2008 Khayyam Publishing, Inc.

Vol.21 • No. 3-4 • 2008
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