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Freezing traveling and rotatingwaves in second order evolution equations

Beyn, Wolf-Jürgen; Otten, Denny; Rottmann-Matthes, Jens

Abstract:
In this paper we investigate the implementation of the so-called freezing method for second order wave equations in one and several space dimensions. The method converts the given PDE into a partial differential algebraic equation which is then solved numerically. The reformulation aims at separating the motion of a solution into a co-moving frame and a profile which varies as little as possible. Numerical examples demonstrate the feasability of this approach for semilinear wave equations with sufficient damping. We treat the case of a traveling wave in one space dimension and of a rotating wave in two space dimensions. In addition, we investigate in arbitrary space dimensions the point spectrum and the essential spectrum of operators obtained by linearizing about the profile, and we indicate the consequences for the nonlinear stability of the wave.


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/1000062696
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-626969
KITopen ID: 1000062696
Verlag KIT, Karlsruhe
Umfang 20 S.
Serie CRC 1173 ; 2016/36
Schlagworte systems of damped wave equations, traveling waves, rotating waves, freezing method, second order evolution equations, point spectra, essential spectra.
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