# Global smooth solution to the standard phase-field model with memory

@article{Colli1997GlobalSS, title={Global smooth solution to the standard phase-field model with memory}, author={Pierluigi Colli and Gianni Gilardi and Maurizio Grasselli}, journal={Advances in Differential Equations}, year={1997}, volume={2}, pages={453-486} }

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## 35 Citations

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…

A P ] 2 8 M ay 2 01 2 Convergence properties for a generalization of the Caginalp phase field system ∗ Giacomo Canevari and Pierluigi Colli

- Mathematics
- 2014

We are concerned with a phase field system consisting of two partial differential equations in terms of the variables thermal displacement, that is basically the time integration of temperature, and…

Convergence properties for a generalization of the Caginalp phase field system

- MathematicsAsymptot. Anal.
- 2013

The aim of this contribution is to investigate the asymptotic behaviour of the problem as the coefficient in front of the Laplacian of the temperature goes to 0, and to discuss the rate of convergence for the difference of the solutions in suitable norms.

Solvability and asymptotic analysis of a generalization of the Caginalp phase field system

- Mathematics
- 2011

We study a diffusion model of phase field type, which consists of a system of two partial differential equations involving as variables the thermal displacement, that is basically the time…

Identification of two memory kernels in a fully hyperbolic phase-field system

- Mathematics
- 2008

Abstract We recover locally in time two (smooth) unknown convolution kernels, depending on time only, in a phase-field system coupling two hyperbolic integro-differential equations, where the…

An inverse problem for a parabolic integrodifferential model in the theory of combustion

- Mathematics
- 2007

Global solution to a singular integro-differential system related to the entropy balance

- Mathematics
- 2007

Convergence of phase field to phase relaxation models governed by an entropy equation with memory

- Mathematics
- 2006

The subject of the present paper consists in proving the convergence of a phase‐field model, based on the entropy equation with memory, to phase relaxation. The well‐posedness and the long‐time…

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…