### 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 |
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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