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Mat. Sb., 2006, Volume 197, Number 5, Pages 99–124 (Mi msb1560)  

This article is cited in 8 scientific papers (total in 8 papers)

Isentropic solutions of quasilinear equations of the first order

M. V. Korobkova, E. Yu. Panovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novgorod State University after Yaroslav the Wise

Abstract: Conditions for the existence of non-trivial isentropic solutions of quasilinear conservation laws are found. Applications to the problem of the functional dependence between partial derivatives of a smooth function of two variables are presented. In particular, necessary conditions on a function $\varphi$ for the equation $\dfrac{\partial v}{\partial t} =\varphi(\dfrac{\partial v}{\partial x})$ to have non-trivial $C^1$-smooth solutions are found.
Bibliography: 13 titles.

DOI: https://doi.org/10.4213/sm1560

Full text: PDF file (591 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:5, 727–752

Bibliographic databases:

UDC: 517.95
MSC: 26B35, 35F20
Received: 04.11.2004 and 13.05.2005

Citation: M. V. Korobkov, E. Yu. Panov, “Isentropic solutions of quasilinear equations of the first order”, Mat. Sb., 197:5 (2006), 99–124; Sb. Math., 197:5 (2006), 727–752

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Korobkov M.V., Panov E.Yu., “Necessary and sufficient conditions for a curve to be an image of the gradient of a $C^1$ function”, Dokl. Math., 74:2 (2006), 696  mathnet  crossref  mathscinet  mathscinet  zmath  isi  elib  elib
    2. Korobkov M.V., “Properties of $C^1$-smooth functions whose gradients have nowhere dense images”, Dokl. Math., 74:2 (2006), 725–727  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. M. V. Korobkov, “Properties of the $C^1$-smooth functions with nowhere dense gradient range”, Siberian Math. J., 48:6 (2007), 1019–1028  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    4. M. V. Korobkov, E. Yu. Panov, “Necessary and sufficient conditions for a curve to be the gradient range of a $C^1$-smooth function”, Siberian Math. J., 48:4 (2007), 629–647  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. M. V. Korobkov, “An example of a $C^1$-smooth function whose gradient range is an arc with no tangent at any point”, Siberian Math. J., 49:1 (2008), 109–116  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. M. V. Korobkov, “Properties of $C^1$-smooth mappings with one-dimensional gradient range”, Siberian Math. J., 50:5 (2009), 874–886  mathnet  crossref  mathscinet  isi  elib  elib
    7. Andreianov B., Donadello C., Ghoshal Sh.S., Razafison U., “on the Attainable Set For a Class of Triangular Systems of Conservation Laws”, J. Evol. Equ., 15:3 (2015), 503–532  crossref  mathscinet  zmath  isi
    8. Ancona F., Glass O., Nguyen Kh.T., “On Kolmogorov Entropy Compactness Estimates For Scalar Conservation Laws Without Uniform Convexity”, SIAM J. Math. Anal., 51:4 (2019), 3020–3051  crossref  mathscinet  zmath  isi
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