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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Multidimensional stability
of planar travelling waves


Author: Todd Kapitula
Journal: Trans. Amer. Math. Soc. 349 (1997), 257-269
MSC (1991): Primary 35B40, 35C15, 35K57
DOI: https://doi.org/10.1090/S0002-9947-97-01668-1
MathSciNet review: 1360225
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Abstract: The multidimensional stability of planar travelling waves for systems of reaction-diffusion equations is considered in the case that the diffusion matrix is the identity. It is shown that if the wave is exponentially orbitally stable in one space dimension, then it is stable for $x\in % \mathbf {R}^n,\,n\ge 2$. Furthermore, it is shown that the perturbation of the wave decays like $t^{-(n-1)/4}$ as $t\to \infty$. The result is proved via an application of linear semigroup theory.


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Additional Information

Todd Kapitula
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Address at time of publication: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131

DOI: https://doi.org/10.1090/S0002-9947-97-01668-1
Received by editor(s): December 15, 1993
Received by editor(s) in revised form: August 30, 1995
Article copyright: © Copyright 1997 American Mathematical Society