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Stable foliations near a traveling front for reaction diffusion systems

Latushkin, Yuri; Schnaubelt, Roland; Yang, Xinyao

Abstract:
We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical kinetics and solid fuel combustion. In this way we complement the orbital stability results from earlier papers by A. Ghazaryan, S. Schecter and Y. Latushkin. The essential spectrum of the differential operator obtained by linearization at the front touches the imaginary axis. In spaces with exponential weights, one can shift the spectrum to the left. We study the nonlinear equation on the intersection of the unweighted and weighted spaces. Small translations of the front form a center unstable manifold. For each small translation we prove the existence of a stable manifold containing the translated front and show that the stable manifolds foliate a small ball centered at the front.


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000056576
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-565766
KITopen ID: 1000056576
Verlag KIT, Karlsruhe
Umfang 21 S.
Serie CRC 1173 ; 2016/18
Schlagworte Combustion problem, traveling wave, stable manifold, foliation
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