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Acta Applicandae Mathematicae

, Volume 137, Issue 1, pp 61–78 | Cite as

Stability of Fronts in Inhomogeneous Wave Equations

Article

Abstract

This paper presents an introduction to the existence and stability of stationary fronts in wave equations with finite length spatial inhomogeneities. The main focus will be on wave equations with one or two inhomogeneities. It will be shown that the fronts come in families. The front solutions provide a parameterisation of the length of the inhomogeneities in terms of the local energy of the potential in the inhomogeneity. The stability of the fronts is determined by analysing (constrained) critical points of those length functions. Amongst others, it will shown that inhomogeneities can stabilise non-monotonic fronts. Furthermore it is demonstrated that bi-stability can occur in such systems.

Keywords

Inhomogeneous wave equation Pinned front Stability 

Mathematics Subject Classification (2010)

34D35 35Q53 37K50 

Notes

Acknowledgements

I would like to thank Arjen Doelman, Stephan van Gils, Chris Knight and Hadi Susanto for sharing their enthusiasm and ideas in our investigations of wave equations with inhomogeneities.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SurreyGuildfordUK

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