### Abstract

The "inflow problem" for a one-dimensional compressible barotropic flow on the half-line R_{+} = (0, +∞) is investigated. Not only classical waves but also the new wave, which is called the "boundary layer solution", arise. Large time behaviors of the solutions to be expected have been classified in terms of the boundary values by [A. Matsumura, Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas, to appear in Proceedings of IMS Conference on Differential Equations from Mechanics, Hong Kong, 1999]. In this paper we give the rigorous proofs of the stability theorems on both the boundary layer solution and a superposition of the boundary layer solution and the rarefaction wave.

Original language | English |
---|---|

Pages (from-to) | 449-474 |

Number of pages | 26 |

Journal | Communications in Mathematical Physics |

Volume | 222 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2001 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*222*(3), 449-474. https://doi.org/10.1007/s002200100517

**Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas.** / Matsumura, Akitaka; Nishihara, Kenji.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 222, no. 3, pp. 449-474. https://doi.org/10.1007/s002200100517

}

TY - JOUR

T1 - Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas

AU - Matsumura, Akitaka

AU - Nishihara, Kenji

PY - 2001

Y1 - 2001

N2 - The "inflow problem" for a one-dimensional compressible barotropic flow on the half-line R+ = (0, +∞) is investigated. Not only classical waves but also the new wave, which is called the "boundary layer solution", arise. Large time behaviors of the solutions to be expected have been classified in terms of the boundary values by [A. Matsumura, Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas, to appear in Proceedings of IMS Conference on Differential Equations from Mechanics, Hong Kong, 1999]. In this paper we give the rigorous proofs of the stability theorems on both the boundary layer solution and a superposition of the boundary layer solution and the rarefaction wave.

AB - The "inflow problem" for a one-dimensional compressible barotropic flow on the half-line R+ = (0, +∞) is investigated. Not only classical waves but also the new wave, which is called the "boundary layer solution", arise. Large time behaviors of the solutions to be expected have been classified in terms of the boundary values by [A. Matsumura, Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas, to appear in Proceedings of IMS Conference on Differential Equations from Mechanics, Hong Kong, 1999]. In this paper we give the rigorous proofs of the stability theorems on both the boundary layer solution and a superposition of the boundary layer solution and the rarefaction wave.

UR - http://www.scopus.com/inward/record.url?scp=0035648890&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035648890&partnerID=8YFLogxK

U2 - 10.1007/s002200100517

DO - 10.1007/s002200100517

M3 - Article

AN - SCOPUS:0035648890

VL - 222

SP - 449

EP - 474

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -