Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Multidimensional stability of planar traveling waves for an integrodifference model

Pages: 741 - 751, Volume 18, Issue 3, May 2013      doi:10.3934/dcdsb.2013.18.741

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Judith R. Miller - Dept. of Mathematics and Statistics, Georgetown University, Washington DC 20057, United States (email)
Huihui Zeng - Mathematical Sciences Center, Tsinghua University, Beijing 100084, China (email)

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.

Keywords:  Traveling waves, stability, integrodifference equation.
Mathematics Subject Classification:  Primary: 45P05, 39A30; Secondary: 47G10, 92D25.

Received: December 2011;      Revised: September 2012;      Available Online: December 2012.