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…
54 Citations
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