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 $\frac{\partial v}{\partial t}=\varphi(\frac{\partial v}{\partial x})$.

**Paper:**- Available as Postscript (280 Kbytes) or gzipped PostScript (94 Kbytes; uncompress using gunzip).
**Author(s):**- M. V. Korobkov, <korob@math.nsc.ru>
- E. Yu. Panov, <pey@novsu.ac.ru>
**Publishing information:****Comments:****Submitted by:**- <pey@novsu.ac.ru> January 1 2005.

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