Geodesic
A note on critical times of $2\times2$ quasilinear hyperbolic systems
Applications of Mathematics, Tome 29 (1984) no. 4, pp. 294-302
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1984.104097
Classification : 35L60, 35L67, 76N10
Keywords: quasilinear hyperbolic system; precise formula; critical time; shock wave; transformation; Riemann invariants; isentropic non-viscous compressible fluid flow 
@article{10_21136_AM_1984_104097,
     author = {Stra\v{s}kraba, Ivan},
     title = {A note on critical times of $2\times2$ quasilinear hyperbolic systems},
     journal = {Applications of Mathematics},
     pages = {294--302},
     year = {1984},
     volume = {29},
     number = {4},
     doi = {10.21136/AM.1984.104097},
     mrnumber = {0754081},
     zbl = {0564.35071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104097/}
}
TY  - JOUR
AU  - Straškraba, Ivan
TI  - A note on critical times of $2\times2$ quasilinear hyperbolic systems
JO  - Applications of Mathematics
PY  - 1984
SP  - 294
EP  - 302
VL  - 29
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104097/
DO  - 10.21136/AM.1984.104097
LA  - en
ID  - 10_21136_AM_1984_104097
ER  - 
%0 Journal Article
%A Straškraba, Ivan
%T A note on critical times of $2\times2$ quasilinear hyperbolic systems
%J Applications of Mathematics
%D 1984
%P 294-302
%V 29
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104097/
%R 10.21136/AM.1984.104097
%G en
%F 10_21136_AM_1984_104097
Straškraba, Ivan. A note on critical times of $2\times2$ quasilinear hyperbolic systems. Applications of Mathematics, Tome 29 (1984) no. 4, pp. 294-302. doi: 10.21136/AM.1984.104097

[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. | DOI | MR | Zbl

[2] A. Jeffrey: Quasilinear Hyperbolic Systems and Waves. Pitman Publishing 1976. | MR | Zbl

[3] F. John: Formation of singularities in one-dimensional nonlinear wave propagation. Comm. Pure Appl. Math., XXVII (1974), 377-405. | DOI | MR | Zbl

[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

Cité par Sources :