Burgers-poisson: A nonlinear dispersive model equation

Klemens Andreas Fellner, Christian Schmeiser

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

A dispersive model equation is considered, which has been proposed by Whitham Linear and Nonlinear Waves, John Wiley & Sons, New York, 1974] as a shallow water model, and which can also be seen as a caricature of two-species Euler-Poisson problems. A number of formal properties as well as similarities to other dispersive equations are derived. A travelling wave analysis and some numerical tests are carried out. The equation features wave breaking in finite time. A local existence result for smooth solutions and a global existence result for weak entropy solutions are proved. Finally, a small dispersion limit is carried out for situations where the solution of the limiting equation is smooth.
OriginalspracheEnglisch
Seiten (von - bis)1509-1525
Seitenumfang17
FachzeitschriftSIAM Journal on Applied Mathematics
Jahrgang64
Ausgabenummer5
DOIs
PublikationsstatusVeröffentlicht - 2004

ÖFOS 2012

  • 1010 Mathematik

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