We discuss the Cauchy problem for the so-called Chaplygin system which often appears in gas, aero- and hydrodynamics. This system can be thought of as a nonlinear analogue of the Cauchy–Riemann system in the plane. We pose Cauchy data on a part of the boundary and apply variational approach to construct a solution to this ill-posed problem. The problem actually gives insight to fundamental questions related to instable problems for nonlinear equations.

People's attitudes towards the law issue and their rights awareness in Ukraine 's regional dimensions basing at the results of nation-wide public opinions surveys by the Institute of Sociology are studied. At the results of the analysis the persistence of regional peculiarities in the respondents' attitudes to the law issues is proved to correlate to the peculiarities of regional political culture, particularly in Donbass and in the Crimea. The author makes the conclusion about the importance of the affirmation of the true rule of law as still an unexplored effective mechanism for the consolidation of democracy and forming Ukrainian civic nation.