Global dynamics of boundary droplets

Peter W. Bates; Jiayin Jin

doi:10.3934/dcds.2014.34.1

Article Contents

2014, Volume 34, Issue 1: 1-17. Doi: 10.3934/dcds.2014.34.1

This issue Previous Article Preface Next Article On the convergence of statistical solutions of the 3D Navier-Stokes-$\alpha$ model as $\alpha$ vanishes

Global dynamics of boundary droplets

Peter W. Bates^1, and
Jiayin Jin^2,

1.
Department of Mathematics, Michigan State University, East Lansing, MI 48824
2.
Department of Mathematics, Michigan State University, East Lansing, MI 48823

Received: November 2012

Revised: April 2013

Published: January 2014

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Abstract

We establish the existence of a global invariant manifold of bubble states for the mass-conserving Allen-Cahn Equation in two space dimensions and give the dynamics for the center of the bubble.

Keywords:

Invariant manifold theory,
bubble solution,
infinitely dimensional dynamical systems,
mass-conserving Allen-Cahn Equation,
global dynamics.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

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References

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