• Corpus ID: 67851741

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}
}

• P. Colli, G. Gilardi, M. Grasselli
• Published 1997
• Mathematics
• Advances in Differential Equations

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 aspects of the approximation to the proof of continuous dependence estimates. In addition, a sufficient condition for the boundedness of the phase variable is given.