| 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 |
| . |
