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

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    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

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    ASJC Scopus subject areas

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

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