A generalization of the Caginalp phase-field system with Neumann boundary conditions (Q393207)
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scientific article; zbMATH DE number 6246143
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A generalization of the Caginalp phase-field system with Neumann boundary conditions |
scientific article; zbMATH DE number 6246143 |
Statements
A generalization of the Caginalp phase-field system with Neumann boundary conditions (English)
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16 January 2014
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type III heat conduction
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well-posedness
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dissipativity
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global attractor
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solid-liquid phase transition
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This paper studies the phase-field system NEWLINE\[NEWLINEu_t-\Delta u +\phi(u)=\alpha_tNEWLINE\]NEWLINE NEWLINE\[NEWLINE\alpha_t-\Delta \alpha_t-\Delta \alpha =-u_t,NEWLINE\]NEWLINE in which \(u\) is an order parameter and \(\alpha_t\) is temperature. This system is a model for solid-liquid phase transition, in which heat conduction follows a law of type III. The system is considered with Neumann boundary conditions on a smooth bounded domain in \(\mathbb R^3\). Under appropriate conditions on the nonlinearity \(\phi\), existence of a compact global attractor for the evolution in the appropriate functional space is proved.
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