Multi-dimensional stability of waves travelling through rectangular lattices in rational directions
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- by A. Hoffman, H. J. Hupkes and E. S. Van Vleck PDF
- Trans. Amer. Math. Soc. 367 (2015), 8757-8808 Request permission
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.References
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Additional Information
- A. Hoffman
- Affiliation: Franklin W. Olin College of Engineering, 1000 Olin Way, Needham, Massachusetts 02492
- MR Author ID: 855186
- Email: aaron.hoffman@olin.edu
- H. J. Hupkes
- Affiliation: Mathematisch Instituut - Universiteit Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
- MR Author ID: 768528
- Email: hhupkes@math.leidenuniv.nl
- E. S. Van Vleck
- Affiliation: Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, Kansas 66045
- MR Author ID: 328628
- Email: erikvv@ku.edu
- 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) - © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3403071