A mathematical analysis of a nonisothermal Allen-Cahn type system

A mathematical analysis of a nonisothermal Allen-Cahn type system

Existence of solutions for a nonisothermal Allen–Cahn type system is proved by using a semidiscrete spectral Galerkin method together with degree theory and maximum principle. Regularity and uniqueness are obtained in a special situation for domains with dimension up to two and smooth enough data. T...

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Veröffentlicht in:Mathematical methods in the applied sciences 2012-08, Vol.35 (12), p.1392-1405
Hauptverfasser: Vaz, C.L.D., Boldrini, J.L.
Format: Artikel
Sprache:eng
Schlagworte:
Allen-Cahn system
binary alloy
Evolution
Galerkin methods
Mathematical analysis
Mathematical models
Maximum principle
Melting
phase field
phase transitions
Solidification
Spectra
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Zusammenfassung:Existence of solutions for a nonisothermal Allen–Cahn type system is proved by using a semidiscrete spectral Galerkin method together with degree theory and maximum principle. Regularity and uniqueness are obtained in a special situation for domains with dimension up to two and smooth enough data. The present system may model the evolution of solidification or melting processes occurring in certain binary alloys. Copyright © 2012 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.2504