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An extension of Glimm’s method to the gas dynamical model of transonic flows. (English) Zbl 1276.35116
The authors study the Cauchy problem for the quasilinear strictly hyperbolic system of conservation laws with one spatial variable. In particular, the compressible Euler equations for the gas flow in time-depending duct are included. The Glimm method is extended to cover a larger class of systems and the transonic flows. The Glimm scheme is coupled with the splitting algorithm. The stability of the scheme is established. Initial data must be considered in non-vacuum states. The entropy solution of bounded variation exists provided that the duct has a positive material derivative.

35L65Conservation laws
35L60Nonlinear first-order hyperbolic equations
35L67Shocks and singularities
76N15Gas dynamics, general
35Q31Euler equations
35L45First order hyperbolic systems, initial value problems
65M12Stability and convergence of numerical methods (IVP of PDE)
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