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A generalization of the Caginalp phase-field system based on the Cattaneo law. (English) Zbl 1167.35304
Summary: We consider in this article a generalization of the Caginalp model for phase transitions based on the Maxwell-Cattaneo law, instead of the classical Fourier law. In particular, we prove the existence and uniqueness of solutions. We finally study the spatial behavior of the solutions in a semi-infinite cylinder.

MSC:
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L70 Second-order nonlinear hyperbolic equations
35K55 Nonlinear parabolic equations
80A22 Stefan problems, phase changes, etc.
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