# Well-posedness of the weak formulation for the phase-field model with memory

@article{Colli1997WellposednessOT, title={Well-posedness of the weak formulation for the phase-field model with memory}, author={Pierluigi Colli and Gianni Gilardi and Maurizio Grasselli}, journal={Advances in Differential Equations}, year={1997}, volume={2}, pages={487-508} }

A phase–field model based on the Gurtin–Pipkin heat flux law is considered. This model consists in a Volterra integrodifferential equation of hyperbolic type coupled with a nonlinear parabolic equation. The system is then associated with a set of initial and Neumann boundary conditions. The resulting problem was already studied by the authors who proved existence and uniqueness of a smooth solution. A careful and detailed investigation on weak solutions is the goal of this paper, going from the…

## 55 Citations

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

- Mathematics
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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,…

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A phase field model is considered when the classical Fourier law is replaced by the linearized GurtinPipkin constitutive assumption for the heat flux. The resulting system of partial differential…

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### Hyperbolic Phase-Field Dynamics with Memory

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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…

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This work is concerned with the study of an initial boundary value problem for a non-conserved phase field system arising from the Penrose-Fife approach to the kinetics of phase transitions. The…

### Convergence of phase field to phase relaxation models with memory

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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…

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