### On Isentropic Solutions of First-Order Quasilinear Equations

M. V. Korobkov and E. Yu. Panov

Abstract: Conditions of existence of nontrivial isentropic solutions to first order conservation laws are found. Applications are given to the problem on functional dependence for partial derivatives of a smooth function of two variables. In particular, we find conditions on the function $\varphi$, which are necessary for existence of nontrivial $C^1$-smooth solutions for the equation $\frac{\partial v}{\partial t}=\varphi(\frac{\partial v}{\partial x})$.

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Author(s):
M. V. Korobkov, <korob@math.nsc.ru>
E. Yu. Panov, <pey@novsu.ac.ru>
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