The initial value problem for some hyperbolic-dispersive system

We consider the initial value problem for some nonlinear hyperbolic‐dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well‐posedness for this system. We also discuss the extension of our res...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Mathematical methods in the applied sciences 2012-01, Vol.35 (2), p.125-133
Hauptverfasser:	Kawashima, Shuichi, Lin, Chi-Kun, Segata, Jun-ichi
Format:	Artikel
Sprache:	eng
Schlagworte:	hyperbolic and dispersive system smoothing effect
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	We consider the initial value problem for some nonlinear hyperbolic‐dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well‐posedness for this system. We also discuss the extension of our results to more general hyperbolic‐dispersive system. Copyright © 2011 John Wiley & Sons, Ltd.
ISSN:	0170-4214 1099-1476
DOI:	10.1002/mma.1542