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Periodic structures in a van der Waals fluid

Published online by Cambridge University Press:  14 November 2011

Paul C. Fife  and
Xiao-Ping Wang
Paul C. Fife
Affiliation:
Mathematics Department, University of Utah, Salt Lake City, Utah 84112, U.S.A.
Xiao-Ping Wang
Affiliation:
Mathematics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
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Abstract

A system of partial differential equations modelling a van der Waals fluid or an elastic medium with nonmonotone pressure-density relation is studied. As the system changes type, regularisations are considered. The existence of one-dimensional periodic travelling waves, with prescribed average density in a certain range, average velocity and wavelength, is proved. They exhibit layer structure when the regularisation parameter is small. Similarities with the Cahn–Hilliard equation are explored.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 235 - 250
Copyright
Copyright © Royal Society of Edinburgh 1998

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