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 - 2012 Jan 30
Externally published	Yes

Keywords

hyperbolic and dispersive system
smoothing effect

ASJC Scopus subject areas

Mathematics(all)
Engineering(all)

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10.1002/mma.1542

Cite this

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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.",

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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.

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KW - smoothing effect

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The initial value problem for some hyperbolic-dispersive system

Abstract

Keywords

ASJC Scopus subject areas

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