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Fundam. Prikl. Mat., 2006, Volume 12, Issue 6, Pages 213–229 (Mi fpm997)  

This article is cited in 3 scientific papers (total in 3 papers)

The Rankine–Hugoniot conditions and balance laws for $\delta$-shocks

V. M. Shelkovich

St. Petersburg State University of Architecture and Civil Engineering

Abstract: New definitions of $\delta$-shock wave-type solutions are introduced for two (one-dimensional) types of hyperbolic systems of conservation laws. Corresponding Rankine–Hugoniot conditions for $\delta$-shocks are derived, and their geometrical interpretation is given. Balance laws connected with “area,” mass, and momentum transportation for $\delta$-shocks are derived.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:1, 2781–2792

Bibliographic databases:

UDC: 517.9

Citation: V. M. Shelkovich, “The Rankine–Hugoniot conditions and balance laws for $\delta$-shocks”, Fundam. Prikl. Mat., 12:6 (2006), 213–229; J. Math. Sci., 151:1 (2008), 2781–2792

Citation in format AMSBIB
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\by V.~M.~Shelkovich
\paper The Rankine--Hugoniot conditions and balance laws for $\delta$-shocks
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 6
\pages 213--229
\mathnet{http://mi.mathnet.ru/fpm997}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2314140}
\zmath{https://zbmath.org/?q=an:1151.35400}
\elib{http://elibrary.ru/item.asp?id=11143816}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 151
\issue 1
\pages 2781--2792
\crossref{https://doi.org/10.1007/s10948-008-0173-y}
\elib{http://elibrary.ru/item.asp?id=13592582}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42449161093}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Shelkovich, “$\delta$- and $\delta'$-shock wave types of singular solutions of systems of conservation laws and transport and concentration processes”, Russian Math. Surveys, 63:3 (2008), 473–546  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Nilsson B., Shelkovich V.M., “Mass, momentum and energy conservation laws in zero-pressure gas dynamics and delta-shocks”, Appl. Anal., 90:11 (2011), 1677–1689  crossref  mathscinet  zmath  isi  elib
    3. E. A. Kolpakova, “O reshenii sistemy uravnenii Gamiltona - Yakobi spetsialnogo vida”, Tr. IMM UrO RAN, 23:1 (2017), 158–170  mathnet  crossref  elib
  • Фундаментальная и прикладная математика
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