### 抜粋

This paper is concerned with asymptotic behavior of solutions of a one-dimensional barotropic flow governed by v_{t} - u_{x} = 0, u_{t} + p(v)_{x} = μ(u_{x}/v)_{x} on R^{1}
_{+} with boundary. The initial data of (v, u) have constant states (v_{+}, u_{+}) at +∞ and the boundary condition at x = 0 is given only on the velocity u, say u_{-}. By virtue of the boundary effect the solution is expected to behave as outgoing wave. Therefore, when u- < u_{+}, v_{-} is determined as (v_{+}, u_{+}) ∈ R_{2}(v_{-}, u_{-}), 2-rarefaction curve for the corresponding hyperbolic system, which admits the 2-rarefaction wave (v^{r}, u^{r})(x/t) connecting two constant states (v_{-}, u_{-}) and (v_{+}, u_{+}). Our assertion is that the solution of the original system tends to the restriction of (v^{r}, u^{r})(x/t) to R^{1}
_{+} as t → ∞ provided that both the initial perturbations and |(v_{+} -v_{-}, u_{+} - u_{-})| are small. The result is given by an elementary L^{2} energy method.

元の言語 | English |
---|---|

ページ（範囲） | 431-441 |

ページ数 | 11 |

ジャーナル | Japan Journal of Industrial and Applied Mathematics |

巻 | 16 |

発行部数 | 3 |

出版物ステータス | Published - 1999 10 |

### フィンガープリント

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### これを引用

*Japan Journal of Industrial and Applied Mathematics*,

*16*(3), 431-441.