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Keywords:
quasilinear hyperbolic system; precise formula; critical time; shock wave; transformation; Riemann invariants; isentropic non-viscous compressible fluid flow
quasilinear hyperbolic system; precise formula; critical time; shock wave; transformation; Riemann invariants; isentropic non-viscous compressible fluid flow
Summary:
In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a $2\times2$ quasilinear hyperbolic system is derived. The applicability of the formula in the engineering praxis is shown on one-dimensional equations of isentropic non-viscous compressible fluid flow.
References:
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[2] A. Jeffrey: Quasilinear Hyperbolic Systems and Waves. Pitman Publishing 1976. MR 0417585 | Zbl 0322.35060
[3] F. John: Formation of singularities in one-dimensional nonlinear wave propagation. Comm. Pure Appl. Math., XXVII (1974), 377-405. DOI 10.1002/cpa.3160270307 | MR 0369934 | Zbl 0302.35064
[4] A. D. Myškis A. M. Filimonov: Continuous solutions of quasi-linear hyperbolic systems with two independent variables. (Russian). Differenciaľnyje uravnenija XVII (1981), 488 - 500.
[5] I. Straškraba V. Jezdinský: Critical times of generating shocks on smooth one-dimensional pressure wakes in inviscid fluids. Acta Technica 28 (1983), No. 5, 629-642. MR 0727520
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