INVESTIGATION OF THE SOLUTION OF A SECOND ORDER PARTIAL DIFFERENTIAL EQUATION OF HYPERBOLIC TYPE

Abstract

In this paper, the initial problem of a second-order partial differential equation is brought to mind by the new method proposed in the paper to a form convenient for applying the method of an additional argument. This method was developed by Kyrgyz scientists. The use of this method is considered in the works of Imanaliev M.I., Pankov P.S., Ashirbaev A.Zh. and other scientists. This method differs from other methods by the introduction of a new additional variable, with the help of which we reduce the problem to a system of integral equations. There are many methods for studying the solution of an integral equations system. At present, the application of the additional argument method for a class of new equations of theoretical and practical interest is relevant. The existence of a unique solution to the initial problem is proved.