Multidimensional stability of planar traveling waves for an integrodifference model

Judith R. Miller; Huihui Zeng

doi:10.3934/dcdsb.2013.18.741

Article Contents

2013, Volume 18, Issue 3: 741-751. Doi: 10.3934/dcdsb.2013.18.741

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Multidimensional stability of planar traveling waves for an integrodifference model

Judith R. Miller^1, and
Huihui Zeng^2,

1.
Dept. of Mathematics and Statistics, Georgetown University, Washington DC 20057
2.
Mathematical Sciences Center, Tsinghua University, Beijing 100084

Received: November 30, 2011

Revised: August 31, 2012

Published: April 2013

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Abstract

This paper studies the multidimensional stability of planar traveling waves for integrodifference equations. It is proved that for a Gaussian dispersal kernel, if the traveling wave is exponentially orbitally stable in one space dimension, then the corresponding planar wave is stable in $H^m(\mathbb{R}^N)$, $N\ge 4$, $m\ge [N/2]+1$, with the perturbation decaying at algebraic rate.

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Mathematics Subject Classification: Primary: 45P05, 39A30; Secondary: 47G10, 92D25.

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