Simulation of Overturning a Wave When a Tsunami Comes Ashore

The paper constructs an exact solution for a system of equations describing one-dimensional and two-dimensional water flows that occur after a wave overturns when a tsunami comes ashore. It is shown that a technique for solving the problem of the breakup of a special discontinuity can be used to describe the wave coming ashore when the depth of the liquid turns to zero at the edge line. Using this technique, solutions of the initial boundary value problem in the vicinity of the edge line in the form of a power series are obtained. The solution of the initial boundary value problem is constructed in the form of power series. The coefficients of the series are found when integrating ordinary differential equations. The theorem on the existence and uniqueness of the solution of the initial boundary value problem is proved.