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

Chapter
Part of the Fields Institute Communications book series (FIC, volume 64)

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.

Keywords

Manifold Liquefaction 

Notes

Acknowledgements

Research of Professor Lin was supported in part by the National Science Foundation under grant DMS-0708386.

Received 6/24/2009; Accepted 4/6/2010

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsGeorgetown UniversityWashingtonUSA
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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