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Steady states of the one-dimensional Cahn–Hilliard equation

Published online by Cambridge University Press:  14 November 2011

A. Novick-Cohen  and
L. A. Peletier
A. Novick-Cohen
Affiliation:
Department of Mathematics, Technion-IIT, Haifa, Israel 32000
L. A. Peletier
Affiliation:
Mathematical Institute, Leiden University, Leiden, The Netherlands
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Synopsis

The steady states of the Cahn–Hilliard equation are studied as a function of interval length, L, and average mass, m. We count the number of nontrivial monotone increasing steady state solutions and demonstrate that if m lies within the spinodal region then for a.e. there is an even number of such solutions and for a.e. there is an odd number of such solutions. If m lies within the metastable region, then for a.e. L > 0 there is an even number of solutions. Furthermore, we prove that for all values of m, there are no secondary bifurcations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1071 - 1098
Copyright
Copyright © Royal Society of Edinburgh 1993

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