### 抄録

The Cauchy problem for the compressible Euler equation is discussed with compactly supported initials. To establish the localexistence of classical solutions by the aid of the theory of quasilinear symmetric hyperbolic systems, a new symmetrization is introduced which works for initials having compact support or vanishing at infinity. It is further shown that as far as the classical solution is concerned, its support does not change, and that the life span is finite for any solution except for the trivial zero solution.

元の言語 | French |
---|---|

ページ（範囲） | 249-257 |

ページ数 | 9 |

ジャーナル | Japan Journal of Applied Mathematics |

巻 | 3 |

発行部数 | 2 |

DOI | |

出版物ステータス | Published - 1986 12 1 |

外部発表 | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)
- Applied Mathematics

### これを引用

*Japan Journal of Applied Mathematics*,

*3*(2), 249-257. https://doi.org/10.1007/BF03167100

**Sur la solution à support compact de l'equation d'Euler compressible.** / Makino, Tetu; Ukai, Seiji; Kawashima, Shuichi.

研究成果: Article

*Japan Journal of Applied Mathematics*, 巻. 3, 番号 2, pp. 249-257. https://doi.org/10.1007/BF03167100

}

TY - JOUR

T1 - Sur la solution à support compact de l'equation d'Euler compressible

AU - Makino, Tetu

AU - Ukai, Seiji

AU - Kawashima, Shuichi

PY - 1986/12/1

Y1 - 1986/12/1

N2 - The Cauchy problem for the compressible Euler equation is discussed with compactly supported initials. To establish the localexistence of classical solutions by the aid of the theory of quasilinear symmetric hyperbolic systems, a new symmetrization is introduced which works for initials having compact support or vanishing at infinity. It is further shown that as far as the classical solution is concerned, its support does not change, and that the life span is finite for any solution except for the trivial zero solution.

AB - The Cauchy problem for the compressible Euler equation is discussed with compactly supported initials. To establish the localexistence of classical solutions by the aid of the theory of quasilinear symmetric hyperbolic systems, a new symmetrization is introduced which works for initials having compact support or vanishing at infinity. It is further shown that as far as the classical solution is concerned, its support does not change, and that the life span is finite for any solution except for the trivial zero solution.

KW - compactly supported solution

KW - compressible Euler equation

KW - non-existence of global solution

KW - quasi-linear symmetric hyperbolic system

UR - http://www.scopus.com/inward/record.url?scp=0000967240&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000967240&partnerID=8YFLogxK

U2 - 10.1007/BF03167100

DO - 10.1007/BF03167100

M3 - Article

VL - 3

SP - 249

EP - 257

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 2

ER -