Asymptotics toward strong rarefaction waves for 2 × 2 systems of viscous conservation laws

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Detail(s)

Original languageEnglish
Pages (from-to)251-282
Journal / PublicationDiscrete and Continuous Dynamical Systems
Volume12
Issue number2
Publication statusPublished - Feb 2005

Abstract

This paper concerns the time asymptotic behavior toward large rarefaction waves of the solution to general systems of 2 × 2 hyperbolic conservation laws with positive viscosity coefficient B(u) 8 <ut + F(u)x = (B(u)ux)x, u ∈ R2, : u(0,x) = u 0(x) → u± as x → ±∞. Assume that the corresponding Riemann problem 8 ut + F(u)x = 0, ( u -1, x <0, u(0,x) = u0r(x) = u+, x > 0 can be solved by one rarefaction wave. If u0(x) in (*) is a small perturbation of an approximate rarefaction wave constructed in Section 2, then we show that the Cauchy problem (*) admits a unique global smooth solution u(t, x) which tends to ur(t, x) as the t tends to infinity. Here, we do not require |u+- - u-| to be small and thus show the convergence of the corresponding global smooth solutions to strong rarefaction waves for 2 × 2 viscous conservation laws.

Research Area(s)

  • 2 × 2 viscous conservation laws, Energy method, Strong rarefaction waves, Strongly coupling condition