# Asymptotic Analysis of a Phase-Field Model with Memory

@article{Colli2019AsymptoticAO, title={Asymptotic Analysis of a Phase-Field Model with Memory}, author={Pierluigi Colli and Gianni Gilardi and Maurizio Grasselli}, journal={Free boundary problems:}, year={2019} }

A phase-field model accounting for memory effects is considered. This model consists of a hyperbolic integrodifferential equation coupled with a parabolic differential inclusion. The latter relation rules the evolution of the phase field and contains a time relaxation parameter which happens to be very small in the appli- cations. A well-posed initial and boundary value problem for the evolution system is introduced and the asymptotic behavior of its solution as the time relaxation goes to zero…

## 10 Citations

### Hyperbolic Phase-Field Dynamics with Memory

- Mathematics
- 2001

Abstract We consider a non-conserved phase-field system which consists of two nonlinearly coupled hyperbolic integrodifferential equations. This model is derived from two basic assumptions: the heat…

### Regularity and convergence results for a phase–field model with memory

- Mathematics
- 1998

A phase field model based on the Coleman-Gurtin heat flux law is considered. The resulting system of non-linear parabolic equations, associated with a set of initial and Neumann boundary conditions,…

### Singular limit of a transmission problem for the parabolic phase-field model

- Mathematics
- 2000

A transmission problem describing the thermal interchange between two regions occupied by possibly different fluids, which may present phase transitions, is studied in the framework of the…

### Uniqueness of Weak Solutions to the Phase-Field Model with Memory

- Mathematics
- 1998

The paper deals with a phase-field model based on the Gurtin-Pipkin heat flux law. A Volterra integrodifferential equation is coupled with a nonlinear parabolic equation in the resulting sys- tem,…

### Applications of Mathematics

- Mathematics
- 2000

A transmission problem describing the thermal interchange between two regions occupied by possibly different fluids, which may present phase transitions, is studied in the framework of the…

### Some asymptotic analysis for hyperbolic relaxed Stefan problems with memory

- Mathematics
- 1999

The aim of this paper is to establish existence and uniqueness of the solution to a diffusive phase transition problem for an integrodifferential energy balance equation of hyperbolic type. We also…

### Identification of two memory kernels and the time dependence of the heat source for a parabolic conserved phase‐field model

- Mathematics
- 2005

In this paper we consider a system of two integro‐differential evolution equations coming from a conservative phase‐field model in which the principal part of the elliptic operators, involved in the…

### Identi cation of two memory kernels and the time dependence of the heat source for a parabolic conserved phase- eld model

- Mathematics
- 2005

In this paper we consider a system of two integro-di erential evolution equations coming from a conservative phaseeld model in which the principal part of the elliptic operators, involved in the two…

### Direct and inverse problems for a parabolic integro-differential system of Caginalp type

- Mathematics
- 2005

In this paper we consider some integro-differential systems of two parabolic PDE’s coming from the Caginalp approach to phase transition models. The first (integrodifferential) equation describes the…

### A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems

- Materials Science
- 2000

We present a bibliography on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems. It contains 5869 titles referring to 588…

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