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2013 | OriginalPaper | Chapter

A Dynamical Systems Approach to Traveling Wave Solutions for Liquid/Vapor Phase Transition

Authors : Haitao Fan, Xiao-Biao Lin

Published in: Infinite Dimensional Dynamical Systems

Publisher: Springer New York

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Abstract

We study the existence of liquefaction and evaporation waves by the methods derived from dynamical systems theory. A traveling wave solution is a heteroclinic orbit with the wave speed as a parameter. We give sufficient and necessary conditions for the existence of such heteroclinic orbit. After analyzing the local unstable and stable manifolds of two equilibrium points, we show that there exists at least one orbit connecting the local unstable manifold of one equilibrium point to the local stable manifold of another equilibrium point. The method is known as the shooting method in the literature.

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previous chapter Spectral Theory for Forward Nonautonomous Parabolic Equations and Applications

next chapter Instability of Radially-Symmetric Spikes in Systems with a Conserved Quantity

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Title: A Dynamical Systems Approach to Traveling Wave Solutions for Liquid/Vapor Phase Transition
Authors: Haitao Fan
Xiao-Biao Lin
Publisher: Springer New York
Book: Infinite Dimensional Dynamical Systems
Print ISBN: 978-1-4614-4522-7

Electronic ISBN: 978-1-4614-4523-4

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-1-4614-4523-4_3

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