# Some properties of solutions of the equation for oil spills spreading on the sea surface

Arkhipov B.V., Shapochkin D.A.

The mathematical modeling of oil spills on the sea surface has recently attracted considerable attention of researchers. Despite the fact that a number of approaches for modeling the main processes of oil transport and transformation on the sea surface are proposed in this area, many of them are not satisfactory and do not correspond to the data of observations and/or experiments. The reason for this is the complexity of these processes, which are complex. In the constructed models, a significant number of acting factors are simultaneously considered and a large number of selected constants are introduced in the expressions used, which leads to difficulties in the analysis (interpretation) of the results. In this regard, there is a need to consider independently the individual processes accompanying the transformation of the oil spill. This paper focuses on the process of oil spill spreading and the movement of its boundary. The approach is based on the solution of the system of partial differential equations (PDE) arising from the consideration of the balance of forces acting on the axisymmetric spot. The aim of the work is to construct a method of numerical solution capable of correctly describing the motion of the contact boundary of the spill. The originality of the proposed approach lies in the fact that, on the one hand, it offers boundary conditions specific to each Fay’s stage, and on the other hand, a method of characteristics is considered to numerical solution of the problem considered. It is shown that the resulting numerical solution is consistent with the Fay’s formulas.characteristics is considered to numerical solution of the problem considered. It is shown that the resulting numerical solution is consistent with the Fay’s formulas.