SOLUTION OF A NONLINEAR DIFFERENTIAL EQUATION IN SECOND-ORDER HYPERBOLIC PARTIAL DERIVATIVES WITH A TIME VARIABLE DERIVATIVE

Abstract

In this paper, we consider the reduction of a non-linear second- order partial differential equation of hyperbolic type with a derivative with respect to the time variable to a system of is integral equations, without reducing the considered equation to a canonical form. First, the equation is reduced to a form convenient for using the additional argument method. Then the method of an additional argument developed scientists of the Kyrgyz Republic is used. When proving the theorem of existence and uniqueness of the solution of the initial problem for a non-linear second-order partial differential equation of hyperbolic type with a derivative with respect to the time variable, a corollary from the principle of Banach contraction mappings is used.