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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Journal d Analyse Ma...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Journal d Analyse Mathématique
Article . 2003 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 2003
Data sources: zbMATH Open
https://dx.doi.org/10.1007/bf0...
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Geometric optics for the Kirchhoff-type equations

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 2003 English Publisher:Springer Science and Business Media LLCJournal:Journal d'Analyse Mathématique, volume 89, pages 57-112 (issn: 0021-7670, eissn: 1565-8538, Copyright policy )
Authors: Yagdjian, Karen;

doi: 10.1007/bf02893077

Geometric optics for the Kirchhoff-type equations

Abstract

The author presents a method for finding small-amplitude, high-frequency wave solutions of Kirchhoff-type hyperbolic systems of nonlocal quasilinear partial differential equations. In this work, the author introduces his main result of the geometric optics on the asymptotic solutions of a first order symmetric strictly hyperbolic system by proving the existence of the uniquely determined solutions \(w_1(t,x)\) and \(w_2(t,x)\).

Related Organizations
Keywords

Kirchhoff-type hyperbolic systems, nonlinear integrodifferential systems, Geometric optics, small-amplitude high-frequency wave solutions, Second-order nonlinear hyperbolic equations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
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