The initial value problem for some hyperbolic-dispersive system

Shuichi Kawashima; Chi Kun Lin; Jun Ichi Segata

doi:10.1002/mma.1542

The initial value problem for some hyperbolic-dispersive system

Shuichi Kawashima
, Chi Kun Lin
, Jun Ichi Segata^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	125-133
Number of pages	9
Journal	Mathematical Methods in the Applied Sciences
Volume	35
Issue number	2
DOIs	https://doi.org/10.1002/mma.1542
Publication status	Published - 30 Jan 2012
Externally published	Yes

Keywords

hyperbolic and dispersive system
smoothing effect

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10.1002/mma.1542

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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 = jan,

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doi = "10.1002/mma.1542",

language = "English",

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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 - https://www.scopus.com/pages/publications/84856274590

U2 - 10.1002/mma.1542

DO - 10.1002/mma.1542

M3 - Article

AN - SCOPUS:84856274590

SN - 0170-4214

VL - 35

SP - 125

EP - 133

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 2

ER -

The initial value problem for some hyperbolic-dispersive system

Abstract

Keywords

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