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Sbornik: Mathematics, 2006, Volume 197, Issue 5, Pages 727–752
DOI: https://doi.org/10.1070/SM2006v197n05ABEH003776 (Mi sm1560) 		 
This article is cited in 9 scientific papers (total in 9 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
English version PDF (356 kB) Citations (9)
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DOI: https://doi.org/10.1070/SM2006v197n05ABEH003776
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 $\dfrac{\partial v}{\partial t} =\varphi\biggl(\dfrac{\partial v}{\partial x}\biggr)$ to have non-trivial $C^1$-smooth solutions are found.
Bibliography: 13 titles.
Received: 04.11.2004 and 13.05.2005
Russian version:
Matematicheskii Sbornik, 2006, Volume 197, Number 5, Pages 99–124
DOI: https://doi.org/10.4213/sm1560
Bibliographic databases:
UDC: 517.95
MSC: 26B35, 35F20
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:7
    References:67
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