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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:
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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