# A note on critical times of $2\times 2$ quasilinear hyperbolic systems

Aplikace matematiky (1984)

- Volume: 29, Issue: 4, page 294-302
- ISSN: 0862-7940

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topStraškraba, Ivan. "A note on critical times of $2\times 2$ quasilinear hyperbolic systems." Aplikace matematiky 29.4 (1984): 294-302. <http://eudml.org/doc/15359>.

@article{Straškraba1984,

abstract = {In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a $2\times 2$ 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.},

author = {Straškraba, Ivan},

journal = {Aplikace matematiky},

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},

language = {eng},

number = {4},

pages = {294-302},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A note on critical times of $2\times 2$ quasilinear hyperbolic systems},

url = {http://eudml.org/doc/15359},

volume = {29},

year = {1984},

}

TY - JOUR

AU - Straškraba, Ivan

TI - A note on critical times of $2\times 2$ quasilinear hyperbolic systems

JO - Aplikace matematiky

PY - 1984

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 29

IS - 4

SP - 294

EP - 302

AB - In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a $2\times 2$ 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.

LA - eng

KW - 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

UR - http://eudml.org/doc/15359

ER -

## References

top- P. D. Lax, 10.1063/1.1704154, J. Math. Physics, Vol. 5 (1964), No. 5, 611 - 613. (1964) Zbl0135.15101MR0165243DOI10.1063/1.1704154
- A. Jeffrey, Quasilinear Hyperbolic Systems and Waves, Pitman Publishing 1976. (1976) Zbl0322.35060MR0417585
- F. John, 10.1002/cpa.3160270307, Comm. Pure Appl. Math., XXVII (1974), 377-405. (1974) Zbl0302.35064MR0369934DOI10.1002/cpa.3160270307
- A. D. Myškis A. M. Filimonov, Continuous solutions of quasi-linear hyperbolic systems with two independent variables, (Russian). Differenciaľnyje uravnenija XVII (1981), 488 - 500. (1981)
- 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. (1983) MR0727520

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