The initial value problem for some hyperbolic-dispersive system

Shuichi Kawashima, Chi Kun Lin, Jun Ichi Segata

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)125-133
Number of pages9
JournalMathematical Methods in the Applied Sciences
Volume35
Issue number2
DOIs
Publication statusPublished - 2012 Jan 30
Externally publishedYes

Fingerprint

Initial value problems
Initial Value Problem
Local Well-posedness
Energy Method
Smoothing
Estimate

Keywords

  • hyperbolic and dispersive system
  • smoothing effect

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

The initial value problem for some hyperbolic-dispersive system. / Kawashima, Shuichi; Lin, Chi Kun; Segata, Jun Ichi.

In: Mathematical Methods in the Applied Sciences, Vol. 35, No. 2, 30.01.2012, p. 125-133.

Research output: Contribution to journalArticle

@article{096d0f05f7f54e5bb0f1988253780381,
title = "The initial value problem for some hyperbolic-dispersive system",
abstract = "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.",
keywords = "hyperbolic and dispersive system, smoothing effect",
author = "Shuichi Kawashima and Lin, {Chi Kun} and Segata, {Jun Ichi}",
year = "2012",
month = "1",
day = "30",
doi = "10.1002/mma.1542",
language = "English",
volume = "35",
pages = "125--133",
journal = "Mathematical Methods in the Applied Sciences",
issn = "0170-4214",
publisher = "John Wiley and Sons Ltd",
number = "2",

}

TY - JOUR

T1 - The initial value problem for some hyperbolic-dispersive system

AU - Kawashima, Shuichi

AU - Lin, Chi Kun

AU - Segata, Jun Ichi

PY - 2012/1/30

Y1 - 2012/1/30

N2 - 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.

AB - 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.

KW - hyperbolic and dispersive system

KW - smoothing effect

UR - http://www.scopus.com/inward/record.url?scp=84856274590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856274590&partnerID=8YFLogxK

U2 - 10.1002/mma.1542

DO - 10.1002/mma.1542

M3 - Article

VL - 35

SP - 125

EP - 133

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 2

ER -