Exponential averaging for traveling wave solutions in rapidly varying periodic media |
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| Authors: | Karsten Matthies Guido Schneider Hannes Uecker |
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| Institution: | 1. Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom;2. Phone: +44 1225 383858, Fax: +44 1225 386492;3. IADM, Universit?t Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany;4. Phone: +49 0711 68565546, Fax: +49 0711 68565535;5. IADM, Universit?t Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, GermanyPhone: +49 0711 68565561, Fax: +49 0711 68565535 |
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| Abstract: | Reaction diffusion systems on cylindrical domains with terms that vary rapidly and periodically in the unbounded direction can be analyzed by averaging techniques. Here, using iterated normal form transformations and Gevrey regularity of bounded solutions, we prove a result on exponential averaging for such systems, i.e., we show that traveling wave solutions can be described by a spatially homogenous equation and exponentially small remainders. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Periodic media averaging exponentially small remainders |
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