# Article

 Title: A note on critical times of $2\times2$ quasilinear hyperbolic systems (English) Author: Straškraba, Ivan Language: English Journal: Aplikace matematiky ISSN: 0373-6725 Volume: 29 Issue: 4 Year: 1984 Pages: 294-302 Summary lang: English Summary lang: Czech Summary lang: Russian . Category: math . 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. (English) Keyword: quasilinear hyperbolic system Keyword: precise formula Keyword: critical time Keyword: shock wave Keyword: transformation Keyword: Riemann invariants Keyword: isentropic non-viscous compressible fluid flow MSC: 35L60 MSC: 35L67 MSC: 76N10 idZBL: Zbl 0564.35071 idMR: MR0754081 DOI: 10.21136/AM.1984.104097 . Date available: 2008-05-20T18:25:22Z Last updated: 2020-07-28 Stable URL: http://hdl.handle.net/10338.dmlcz/104097 . Reference: [1] P. D. Lax: Development of singularities of solutions of nonlinear hyperbolic partial differential equations.J. Math. Physics, Vol. 5 (1964), No. 5, 611 - 613. Zbl 0135.15101, MR 0165243, 10.1063/1.1704154 Reference: [2] A. Jeffrey: Quasilinear Hyperbolic Systems and Waves.Pitman Publishing 1976. Zbl 0322.35060, MR 0417585 Reference: [3] F. John: Formation of singularities in one-dimensional nonlinear wave propagation.Comm. Pure Appl. Math., XXVII (1974), 377-405. Zbl 0302.35064, MR 0369934, 10.1002/cpa.3160270307 Reference: [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. Reference: [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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