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The Penrose–Fife-type equations: counting the one-dimensional stationary solutions

Published online by Cambridge University Press:  14 November 2011

A. Novick-Cohen  and
Songmu Zheng
A. Novick-Cohen
Affiliation:
Department of Mathematics, Technion-IIT, Haifa, Israel32000
Songmu Zheng
Affiliation:
Department of Mathematics, Institute of Mathematics, Fudan University, Shanghai 200433, China
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Extract

A method for counting the solutions for Penrose–Fife-type phase field equations is derived. The method used is similar to that developed recently for obtaining a precise count for the number of solutions for the Cahn–Hilliard equation [9], and is based on the derivation of an extended system of Picard–Fuchs equations as well as on estimates obtained in [11]. The Penrose–Fife-type phase field equations represent a thermodynamically consistent model for phase separation of a conserved order parameter (typically concentration) in binary systems in which latent heat effects are important in the phase separation process.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 3 , 1996 , pp. 483 - 504
Copyright
Copyright © Royal Society of Edinburgh 1996

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