The spread of an oil slick in the sea is considered. A mathematical model of the process is proposed and a formulas for determining the oil slick sizes in explicit form are obtained.

The process of nonstationary incompressible nonlinear-viscous liquid fl ow through a pipeline is considered. It is described by a parabolic-type one-dimensional nonlinear equation. The problem of determining the dependence of the pressure difference on time from the assigned volumetric fl ow rate in the given pipeline is formulated. Such a problem pertains to the class of inverse problems connected with the restoration of the dependence of the right-hand sides of parabolic equations on time. A computational algorithm for solving the problem has been suggested.Introduction. At the present time, pipeline transportation is the main form of conveying nonlinear-viscous fl uids. Usually, in designing pipelines the following parameters are specifi ed: the fl uid fl ow rate, which is the basic characteristic of the pipeline capacity in conformity with its function, and the location of the pipeline beginning and end. Here, among the particular concerns of the present work, is the determination of the pressure difference needed for the transportation of the specifi ed fl uid fl ow through the given pipeline. In practice, for solving such a problem, use is mainly made of the differential equations of stationary nonlinear-viscous fl uid fl ow through a pipeline [1-3]. However, for the pipeline transport operation it is important to carry out investigations on determination of the dependence of pressure difference on the fl uid fl ow rate for transported nonstationary nonlinear-viscous fl uid fl ows. This work presents a numerical method of determining such a dependence by solving an inverse problem for the equation of nonstationary nonlinear-viscous fl uid fl ow in a pipeline.Formulation of the Problem. Let there be a horizontal rigid-walled pipeline of radius R and length l with an incompressible nonlinear-viscous fl uid pumped through it. The rheological equation of the fl uid has the form

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