Semi-hyperbolic patches arising from a transonic shock in simple waves interaction
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In this paper we consider a Riemann problem, in particular, the case of the presence of the semi-hyperbolic patches arising from a transonic shock in simple waves interaction. Under this circumstance, we construct global solutions of the two-dimensional Riemann problem of the pressure gradient system. We approach the problem as a Goursat boundary value problem and a mixed initial-boundary value problem, where one of the boundaries is the transonic shock.
Abstract
In this paper we consider a Riemann problem, in particular, the case of the presence of the semi-hyperbolic patches arising from a transonic shock in simple waves interaction. Under this circumstance, we construct global solutions of the two-dimensional Riemann problem of the pressure gradient system. We approach the problem as a Goursat boundary value problem and a mixed initial-boundary value problem, where one of the boundaries is the transonic shock.
참고문헌 (10)
- Z. Dai, "Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics", Arch. Ration. Mech. Anal, 155(4), pp.277~298 (2000)
- J. Glimm, "Transonic shock formation in a rarefaction Riemann problem for the 2D compressible Euler equations", SIAM J. Appl. Math, 69(3), pp.720~742 (2008)
- J. Li, "The Two-dimensional Riemann Problem in Gas Dynamics" (1998), Addison Wesley Longman limited
- J. Li, "Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations", Comm. Math. Phys, 267(1), pp.1~12 (2006)
- K. Song, "A pressure-gradient system on non-smooth domains", Comm. Partial Differential Equations, 28, pp.199~221 (2003)
- K. Song, "Semi-hyperbolic patches of the pressure gradient system", Disc. Cont. Dyna. Syst. Series A, 24, pp.1365~1380 (2009)
- R.-H. Wang, "Existence and uniqueness of solutions for some mixed initial boundary value problems of quasilinear hyperbolic systems in two independent variables", Acta Sci. Natur. Jilin University, 2, pp.277~298 (1963)
- Y. Zheng, "Two-dimensional regular shock reflection for the pressure gradient system of conservation laws", Acta Math. Appl. Sin. Engl. Ser, 22(2), pp.177~210 (2006)
- Y. Zheng, "Systems of Conservation Laws: Two-Dimensional Riemann Problems", PNLDE, 38 (2001)
- Y. Zheng, "The compressible Euler system in two space dimensions. Nonlinear conserva- tion laws, fluid systems and related topics", pp.301~390 (2009), World Sci. Publishing