SOLUTION OF A SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES WITH THREE INDEPENDENT VARIABLES

Abstract

At present time, the method of an additional argument is being developed, which makes it possible in principle to reduce various types of nonlinear partial differential equations to integral equations, and at the same time, on the basis of this method, the existence of solutions to a wide range of problems in the theory of dynamical systems is proved. There is considered a system of nonlinear partial differential equations of the first order with three independent variables. The existence of a unique solution to the initial problem is proved by the method of an additional argument. Based on the results obtained, it is possible to construct a solution to a specific problem. This method can also be used to study solutions to other systems of differential equations.