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Miranville, Alain; Quintanilla, Ramon

A generalization of the Caginalp phase-field system based on the Cattaneo law. (English) Zbl 1167.35304

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 5-6, 2278-2290 (2009).
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.

Cited in 31 Documents

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.

Keywords:

Caginalp system; Maxwell-Cattaneo law; well-posedness; stability; spatial behavior of the solutions; semi-infinite cylinder
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\textit{A. Miranville} and \textit{R. Quintanilla}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 5--6, 2278--2290 (2009; Zbl 1167.35304)
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References:

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