Differential and Integral Equations

On a doubly nonlinear phase-field model for first-order transitions with memory

V. Berti, M. Fabrizio, and C. Giorgi

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


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.

Article information

Differential Integral Equations, Volume 21, Number 3-4 (2008), 325-350.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35G30: Boundary value problems for nonlinear higher-order equations
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]


Berti, V.; Fabrizio, M.; Giorgi, C. On a doubly nonlinear phase-field model for first-order transitions with memory. Differential Integral Equations 21 (2008), no. 3-4, 325--350. https://projecteuclid.org/euclid.die/1356038783

Export citation