## Differential and Integral Equations

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

#### Abstract

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

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

Dates
First available in Project Euclid: 20 December 2012