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DOI: 10.5445/IR/1000088283
Veröffentlicht am 05.12.2018

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.


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: 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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