Asymptotic behavior of a one-dimensional compressible viscous gas with free boundary

Tao Pan*, Hongxia Liu, Kenji Nishihara


    研究成果: Article査読

    13 被引用数 (Scopus)


    We consider the initial-boundary value problem for a one-dimensional compressible viscous gas with free boundary, which is modeled in the Eulerian coordinate as (IBVP) { ρ + (ρu)x = 0, x > x(t), t > 0, (ρu)t + (ρu2 + p)x = μuxx, x > x(t), t > 0, (p - μux)|x=x(t) = p0, dx(t)/dt = u(x(t),t), t ≥ 0, (ρ, u)|t=0 = (ρ0, u0)(x), x ≥ x(0). Here, ρ(> 0) is the density, u is the velocity, p = p(ρ) = ργ (γ ≥ 1: the adiabatic constant) is the pressure, and μ(> 0) is the viscosity constant. At the boundary the flow is attached to the atmosphere with pressure p0 (> 0) and the boundary condition is derived by the balance law. The initial data have constant states (ρ+, u+) at x = ∞. The flow has no vacuum state so that ρ0(x) > 0 and ρ+ > 0 are assumed. Our main purpose is to investigate the asymptotic behaviors of solutions for (IBVP), which are closely related to those for the corresponding Cauchy problem and hence the corresponding Riemann problem. Depending on p0 and the endstates (ρ+, u+), the solutions are shown to tend to the outgoing rarefaction wave or the outgoing viscous shock wave as t tends to infinity. The proof is given under the weakness assumption of the waves. The analysis will be done by changing (IBVP) into the problem in the Lagrangian coordinate.

    ジャーナルSIAM Journal on Mathematical Analysis
    出版ステータスPublished - 2003

    ASJC Scopus subject areas

    • 数学 (全般)
    • 分析
    • 応用数学


    「Asymptotic behavior of a one-dimensional compressible viscous gas with free boundary」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。