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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
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
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
Linking options:
https://www.mathnet.ru/eng/sm1560https://doi.org/10.1070/SM2006v197n05ABEH003776 https://www.mathnet.ru/eng/sm/v197/i5/p99
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Abstract page: | 569 | Russian version PDF: | 228 | English version PDF: | 10 | References: | 71 | First page: | 2 |
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