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Singular shock waves in interactions
Author(s):
Marko
Nedeljkov
Journal:
Quart. Appl. Math.
66
(2008),
281-302.
MSC (2000):
Primary 35L65, 35L67
Posted:
February 7, 2008
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Abstract:
In a number of papers it has been shown that there exist one-dimensional systems such that they contain solutions with so-called overcompressive singular shock waves besides the usual elementary waves (shock and rarefaction waves as well as contact discontinuities). One can see their definition for a general 2  2 system with fluxes linear in one of the dependent variables in Nedeljkov, Delta and singular delta locus for one dimensional systems of conservation laws, Math. Method Appl. Sci. 27 (2004), 931-955. This paper is devoted to examining their interactions with themselves and elementary waves. After a discussion of systems given in a general form, a complete analysis will be given for the ion-acoustic system given in Keyfitz and Kranzer, Spaces of weighted measures for conservation laws with singular shock solutions, J. Differ. Equations 118 (1995), no. 2, 420-451.
References:
-
- 1.
- A. Bressan, Hyperbolic Systems of Conservation Laws, Oxford University Press, New York, 2000. MR 1816648 (2002d:35002)
- 2.
- C. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, Heidelberg, 2000. MR 1763936 (2001m:35212)
- 3.
- V. G. Danilov and V. M. Shelkovich, Dynamics of propagation and interaction of shock waves in conservation law systems, J. Differ. Equations 211 (2005), 333-381. MR 2125546 (2006f:35173)
- 4.
- -, Delta-shock wave type solution of hyperbolic systems of conservation laws, Q. Appl. Math. 29 (2005), 401-427. MR 2169026 (2006j:35158)
- 5.
- F. Huang, Weak solution to pressureless type system, Comm. Partial Differential Equations 30 (2005), no. 1-3, 283-304. MR 2131055 (2005k:35263)
- 6.
- B. L. Keyfitz and H. C. Kranzer, Spaces of weighted measures for conservation laws with singular shock solutions, J. Differ. Equations 118 (1995), no. 2, 420-451. MR 1330835 (96b:35138)
- 7.
- P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, 1973. MR 0350216 (50:2709)
- 8.
- M. Nedeljkov, Delta and singular delta locus for one dimensional systems of conservation laws, Math. Method Appl. Sci. 27 (2004), 931-955. MR 2055283 (2005g:35210)
- 9.
- M. Nedeljkov and M. Oberguggenberger, Delta shock wave and interactions in a simple model case, Submitted.
- 10.
- Tan, D., Zhang, T. and Zheng, Y., Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws, J. Differ. Equations 112 (1994), 1-32. MR 1287550 (95g:35124)
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Additional Information:
Marko
Nedeljkov
Affiliation:
Department of Mathematics and Informatics, University of Novi Sad, Trg D. Obradovica 4, 21000 Novi Sad, Yugoslavia
Email:
markonne@uns.ns.ac.yu, marko@im.ns.ac.yu
PII:
S0033-569X-08-01109-5
Keywords:
conservation law systems,
singular shock wave,
interaction of singularities
Received by editor(s):
June 10, 2006
Posted:
February 7, 2008
Additional Notes:
The work is supported by Serbian Ministry of Science and Enviroment Protection, Grant No. 144016
Copyright of article:
Copyright
2008,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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