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

Akitaka Matsumura, Kenji Nishihara

    Research output: Contribution to journalArticle

    70 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)449-474
    Number of pages26
    JournalCommunications in Mathematical Physics
    Volume222
    Issue number3
    DOIs
    Publication statusPublished - 2001

    Fingerprint

    Large Time Behavior
    One-dimensional System
    Behavior of Solutions
    half spaces
    Half-space
    Boundary Layer
    boundary layers
    gases
    Rarefaction Wave
    barotropic flow
    Stability Theorem
    Compressible Flow
    International Magnetospheric Study
    One-dimensional Model
    Hong Kong
    Boundary Value
    Superposition
    Mechanics
    Half line
    elastic waves

    ASJC Scopus subject areas

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

    Cite this

    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.

    In: Communications in Mathematical Physics, Vol. 222, No. 3, 2001, p. 449-474.

    Research output: Contribution to journalArticle

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