Nonlinear Stochastic Models for Water Level Dynamics in Closed Lakes

This paper presents the results of investigation of nonlinear mathematical models of the behavior of closed lakes using the example of the Caspian Sea. Forecasting the level of the Caspian Sea is crucial both for the economy of the region and for the region's environment. The Caspian Sea is a closed reservoir; it is well known that its level changes considerably due to a variety of factors including global climate change. A series of forecasts exists based on different methods and taking into account some of the following factors: the influence of the sun's activity; the atmospheric circulation; the changing shape of the world's ocean; geological phenomena; the river inflow; and the velocity of evaporation. All of these models were calculated based on the linearization of the relations considered. For the last two decades, the most popular model has been the linear stochastic equation of water balance. This model was used as the base of the well known project of reversing the flow of the northward-flowing rivers. But the real behavior of the Caspian Sea contradicted the forecasting done using this model. One of the reasons of the failure was ignorance of the relations mentioned above. We are inclined to think however that the main reason for failure was that the forecast used a linear equation. The goal of the present paper is to analyze and generalize, from the modern mathematical point of view, the forecasting methodology for the level of the Caspian Sea, including the nonlinear effects crucial influence on the dynamics of sea level. In particular, the mathematical problems concerning the nonlinear stochastic equations are considered

The analytical solution of Newton’s aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary

The method of Hessian measures is used to find the differential equation that defines the optimal shape of nonrotationally symmetric bodies with minimal resistance moving in a rare medium. The synthesis of optimal solutions is described. A theorem on the optimality of the obtained solutions is proved