Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Singular shock waves in interactions

Author: Marko Nedeljkov
Journal: Quart. Appl. Math. 66 (2008), 281-302
MSC (2000): Primary 35L65, 35L67
DOI: https://doi.org/10.1090/S0033-569X-08-01109-5
Published electronically: February 7, 2008
MathSciNet review: 2416774
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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 $ \times$ 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.

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Additional Information

Marko Nedeljkov
Affiliation: Department of Mathematics and Informatics, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, Yugoslavia
Email: markonne@uns.ns.ac.yu, marko@im.ns.ac.yu

DOI: https://doi.org/10.1090/S0033-569X-08-01109-5
Keywords: conservation law systems, singular shock wave, interaction of singularities
Received by editor(s): June 10, 2006
Published electronically: February 7, 2008
Additional Notes: The work is supported by Serbian Ministry of Science and Enviroment Protection, Grant No. 144016
Article copyright: © Copyright 2008 Brown University
The copyright for this article reverts to public domain 28 years after publication.