Abstract
This paper is devoted to analytical methods for solving shallow water equations which simulate water flows when a tsunami comes ashore in the two-dimensional case. The currents are considered near the edge boundary, which for the two-dimensional model is the point of intersection of the water surface with the shore. In order to do this, the system of equations is rewritten in a polar coordinate system with a center at the corner point of the edge boundary. Then the independent variable and unknown function switch roles. An alternative is proved for the resulting system: the motion of the edge boundary is determined from the solutions of a nonlinear system of partial differential equations, or at the edge boundary the derivative of an unknown function is equal to infinity. In order to construct a solution, a power series is compiled, the coefficients of which are solutions of ordinary differential equations. The existence and uniqueness theorem of a solution constructed as a series with analytical boundary conditions is substantiated.
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