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.",

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author = "Shuichi Kawashima and Lin, {Chi Kun} and Segata, {Jun Ichi}",

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AU - Segata, Jun Ichi

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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.

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KW - smoothing effect

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

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The initial value problem for some hyperbolic-dispersive system

Abstract

Keywords

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