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Effective slow dynamics models for a class of dispersive systems

Baumstark, Simon; Schneider, Guido; Schratz, Katharina; Zimmermann, Dominik

Abstract:
We consider dispersive systems of the form
∂_t U = Λ_U U + B_U (U, V ), ε∂_t V = Λ_V V + B_V (U, U )
in the singular limit ε → 0, where Λ_U , Λ_V are linear and B_U, B_V bilinear mappings. We are interested in deriving error estimates for the approximation obtained through the regular limit system
∂_t ψ_U = Λ_U ψ_U − B_U (ψ_U , Λ^{−1}_V B_V (ψ_U, ψ_U ))
from a more general point of view. Our abstract approximation theorem applies to a number of semilinear systems, such as the Dirac-Klein-Gordon system, the Klein-Gordon-Zakharov system, and a mean field polaron model. It extracts the common features of scattered results in the literature, but also gains an approximation result for the Dirac-Klein-Gordon system which has not been documented in the literature before. We explain that our abstract approximation theorem is sharp in the sense that there exists a quasilinear system of the same structure where the regular limit system makes wrong predictions.

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Volltext §
DOI: 10.5445/IR/1000088283
Veröffentlicht am 05.12.2018
Coverbild
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
urn:nbn:de:swb:90-882837
KITopen-ID: 1000088283
Verlag KIT, Karlsruhe
Umfang 28 S.
Serie CRC 1173 ; 2018/40
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagworte slow fast system, approximation, KGZ system
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