Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-15T09:44:14.711Z Has data issue: false hasContentIssue false
  • English
  • Français

Reflection and transmission of discontinuity waves through a shock wave. General theory including also the case of characteristic shocks

Published online by Cambridge University Press:  14 November 2011

Guy Boillatt  and
Tommaso Ruggeri
Guy Boillatt
Affiliation:
Istituto di Matematica della Università di Bologna, Italy
Tommaso Ruggeri
Affiliation:
Istituto di Matematica della Università di Bologna, Italy
Get access Rights & Permissions [Opens in a new window]

Synopsis

An incident wave creates a discontinuity in the acceleration of the shock front. The amplitudes of the reflected and transmitted waves are also determined. Special attention is given to the case of the weak shocks and the characteristic shocks.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 1-2 , 1979 , pp. 17 - 24
Copyright
Copyright © Royal Society of Edinburgh 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Jeffrey, A.. The propagation of weak discontinuities in quasi-linear hyperbolic systems with discontinuous coefficients. I. Fundamental theory. Applicable Anal. 3 (1973), 79–100.CrossRefGoogle Scholar
2Jeffrey, A.. The propagation of weak discontiniuties in quasi-linear hyperbolic systems with discontinuous coefficients. II. Special cases and application. Applicable Anal. 3 (1973/1974), 359–375.CrossRefGoogle Scholar
3Jeffrey, A.. Quasilinear hyperbolic systems and waves (London: Pitman, 1976).Google Scholar
4Boillat, G.. La propagation des ondes (Paris: Gauthier-Villars, 1965).Google Scholar
5Boillat, G.. Ondes asymptotiques non linéaires. Ann. Mat. Pura Appl. 111 (1976), 31–44.CrossRefGoogle Scholar
6Brun, L.. Ondes de choc finies dans les solides élastiques, In Mechanical waves in solids, eds Mandel, J. and Brun, L. (Vienna: Springer, 1975).Google Scholar
7Lax, P. D.. Hyperbolic systems of conservation laws, II. Comm. Pure Appl. Math. 10 (1957), 537–566.CrossRefGoogle Scholar
8Jeffrey, A. and Taniuti, T.. Nonlinear wave propagation with applications to physics and mag-netohydrodynamics (New York and London: Academic Press, 1964).Google Scholar
9Boillat, G.. Sur une fonction croissante comme l'entropie et génératrice des chocs dans les systèmes hyperboliques. C.R. Acad. Sci. Paris Sér. A 283 (1976), 409–412.Google Scholar
10Boillat, G.. Chocs caractéristiques. C.R. Acad. Sci. Paris Sér. A 274 (1972), 1018–1021.Google Scholar
11Boillat, G.. Discontinuités de contact. C.R. Acad. Sci. Paris Sér. A 275 (1972), 1255–1258.Google Scholar
12Boillat, G.. Chocs caractéristiques et ondes simples exceptionnelles pour les systèmes conservatifs à intégrale d'énergie: forme explicite de la solution. C.R. Acad. Sci. Paris Sér. A 280 (1975), 1325–1328.Google Scholar
13Boillat, G.. Evolution des chocs caractéristiques dans les champs dérivant d'un principe variationnel. J. Math. Pures Appl. 56 (1977), 137–147.Google Scholar
14Boillat, G.. Sur la croissance des ondes simples et l'instabilité de chocs caractéristiques des systèmes hyperboliques avec application à la discontinuité de contact d'un fluide. C.R. Acad. Sci. Paris Sér. A 284 (1977), 1481–1484.Google Scholar
15Strumia, A.. Transmission and reflexion of a discontinuity wave through a characteristic shock in non linear optics. Riv. Mat. Univ. Parma 4 (1978), in press.Google Scholar