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Exponential averaging for traveling wave solutions in rapidly varying periodic media
Author(s) -
Matthies Karsten,
Schneider Guido,
Uecker Hannes
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410490
Subject(s) - traveling wave , mathematics , iterated function , exponential function , exponential growth , bounded function , reaction–diffusion system , mathematical analysis , diffusion , exponential decay , physics , thermodynamics , nuclear physics
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)