Displaying similar documents to “Singular limit of a transmission problem for the parabolic phase-field model”

Hysteresis operators in phase-field models of Penrose-fife type

Pavel Krejčí, Jürgen Sprekels (1998)

Applications of Mathematics

Similarity:

Phase-field systems as mathematical models for phase transitions have drawn a considerable attention in recent years. However, while they are suitable for capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors have recently proposed a new approach to phase-field models which is based on the mathematical...

Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method

Jindřich Nečas, Tomáš Roubíček (1990)

Aplikace matematiky

Similarity:

The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the...

On a phase transition model of Penrose-Fife type

Gianni Gilardi (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

We deal with a Penrose-Fife type model for phase transition. We assume a rather general constitutive low for the heat flux and treat the Dirichlet and Neumann boundary condition for the temperature. Some of our proofs apply to different types of boundary conditions as well and improve some results existing in the literature.

Global existence of weak solutions to the Fried-Gurtin model of phase transitions

Zenon Kosowski (2007)

Applicationes Mathematicae

Similarity:

We prove the existence of global in time weak solutions to a three-dimensional system of equations arising in a simple version of the Fried-Gurtin model for the isothermal phase transition in solids. In this model the phase is characterized by an order parameter. The problem considered here has the form of a coupled system of three-dimensional elasticity and parabolic equations. The system is studied with the help of the Faedo-Galerkin method using energy estimates.