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Mass, momentum and energy conservation laws in zero-pressure gas dynamics and delta-shocks. (English) Zbl 1237.35111
The authors study delta shock type solutions for the one-dimensional system of zero-pressure gas dynamics. They establish the Rankine-Hugoniot relations on the delta shock wave front and derive the balance relations describing mass, momentum and energy transportation.

MSC:
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
76L05 Shock waves and blast waves in fluid mechanics
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[1] Evans LC, Partial Differential Equations (1998)
[2] DOI: 10.1007/s00205-007-0061-9 · Zbl 1153.90003 · doi:10.1007/s00205-007-0061-9
[3] Bouchut F, Series on Advances in Mathematics for Applied Sciences, ’Advances in Kinetic Theory and Computing’ 22 pp 171– (1994)
[4] DOI: 10.1137/S0036141001399350 · Zbl 1038.35035 · doi:10.1137/S0036141001399350
[5] DOI: 10.1016/j.physd.2003.09.039 · Zbl 1098.76603 · doi:10.1016/j.physd.2003.09.039
[6] Danilov VG, Quart. Appl. Math. 63 pp 401– (2005)
[7] DOI: 10.1016/j.jde.2004.12.011 · Zbl 1072.35121 · doi:10.1016/j.jde.2004.12.011
[8] DOI: 10.1007/BF02101897 · Zbl 0852.35097 · doi:10.1007/BF02101897
[9] Albeverio S, Analytical Approaches to Multidimensional Balance Laws, Ch. 2 (Ed. O.S. Rozanova) pp 45– (2005)
[10] DOI: 10.1016/j.jmaa.2008.03.040 · Zbl 1155.35059 · doi:10.1016/j.jmaa.2008.03.040
[11] J. Li and T. Zhang,On the initial-value problem for zero-pressure gas dynamics, hyperbolic problems: Theory, numerics, applications, Seventh International Conference in Zürich, February 1998, Birkhäuser Verlag, Basel, Boston, Berlin, 1999, pp. 629–640. · Zbl 0926.35120
[12] Shelkovich VM, Uspekhi Mat. Nauk 63 pp 73– (2008) · doi:10.4213/rm9196
[13] Shen W, Mem. Amer. Math. Soc. 137 pp 1– (1999)
[14] DOI: 10.1006/jdeq.1999.3629 · Zbl 0948.35079 · doi:10.1006/jdeq.1999.3629
[15] DOI: 10.1016/j.jde.2006.04.004 · Zbl 1108.35116 · doi:10.1016/j.jde.2006.04.004
[16] DOI: 10.1016/j.jde.2006.08.003 · Zbl 1108.35117 · doi:10.1016/j.jde.2006.08.003
[17] Shelkovich VM, Fundament. Priklad. Mat. 12 pp 213– (2006)
[18] DOI: 10.1103/RevModPhys.61.185 · doi:10.1103/RevModPhys.61.185
[19] Zeldovich YaB, Astron. Astrophys. 5 pp 84– (1970)
[20] DOI: 10.1016/0021-8928(79)90102-3 · Zbl 0443.73017 · doi:10.1016/0021-8928(79)90102-3
[21] Kraiko AN, Priklad. Mat. Mekh. 47 pp 619– (1983)
[22] Kraiko AN, Priklad. Mat. Mekh. 46 pp 96– (1982)
[23] Kanwal Ram P, Generalized Functions: Theory and technique (1998)
[24] Gel’fand IM, Properties and Operations 1 (1964)
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