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Transactions of the American Mathematical Society

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

 
 

 

Multi-dimensional stability of waves travelling through rectangular lattices in rational directions


Authors: A. Hoffman, H. J. Hupkes and E. S. Van Vleck
Journal: Trans. Amer. Math. Soc. 367 (2015), 8757-8808
MSC (2010): Primary 34K31, 37L15
DOI: https://doi.org/10.1090/S0002-9947-2015-06392-2
Published electronically: February 19, 2015
MathSciNet review: 3403071
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Abstract: We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small perturbations. We employ recently developed techniques involving pointwise Green's functions estimates for functional differential equations of mixed type (MFDEs), allowing our results to be applied even in situations where comparison principles are not available.


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Additional Information

A. Hoffman
Affiliation: Franklin W. Olin College of Engineering, 1000 Olin Way, Needham, Massachusetts 02492
Email: aaron.hoffman@olin.edu

H. J. Hupkes
Affiliation: Mathematisch Instituut - Universiteit Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Email: hhupkes@math.leidenuniv.nl

E. S. Van Vleck
Affiliation: Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, Kansas 66045
Email: erikvv@ku.edu

DOI: https://doi.org/10.1090/S0002-9947-2015-06392-2
Keywords: Travelling waves, multidimensional lattice differential equations, Green's functions, nonlinear stability, Fourier synthesis
Received by editor(s): September 27, 2012
Received by editor(s) in revised form: January 16, 2014
Published electronically: February 19, 2015
Additional Notes: The first author acknowledges support from the NSF (DMS-1108788)
The second author acknowledges support from the Netherlands Organization for Scientific Research (NWO)
The third author acknowledges support from the NSF (DMS-0812800 and DMS-1115408)
Article copyright: © Copyright 2015 American Mathematical Society

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