# American Institute of Mathematical Sciences

May  2013, 18(3): 741-751. doi: 10.3934/dcdsb.2013.18.741

## Multidimensional stability of planar traveling waves for an integrodifference model

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

Received  December 2011 Revised  September 2012 Published  December 2012

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.
Citation: Judith R. Miller, Huihui Zeng. Multidimensional stability of planar traveling waves for an integrodifference model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (3) : 741-751. doi: 10.3934/dcdsb.2013.18.741
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