Abstract:
The investigation of a system of first-order nonlinear partial differential equations by the method of characteristics
reduces to the study of a nonlinear system of integral equations, where a superposition of unknown functions is always present.
After finding a solution in the characteristic variables, in order to obtain the solution of the original problem, it is required to
go from the characteristic variables to the original variables. The latter problem in many cases is so complex that it is
unsolvable, but accept the possibility of inverse transformation of variables as a condition.
The aim of this paper is to investigate solutions of a system of nonlinear differential equations in first-order partial
derivatives with many variable methods by an additional argument, by means of which the system of equations considered is
reduced to systems of integral equations. In this case, the superposition of unknown functions is not present in the system of
integral equations. The existence of a solution of integral equations system is proved with a more rigorous method of writing
operators in function spaces using the principle of "contracting mappings" for operators of a retarded type
Keywords:partial differential equation, system of equations, initial conditions, additional argument, delayed type operator, the principle of contracting mappings.
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