Abstract:
This article examines the integrals of systems of partial derivative equations. A new method of finding integrals of random systems of partial differential equations is suggested. It is shown that, if they exist, their appearance is finally determined from solutions of parametric ordinary differential equations. And also they can be found analytically from the solution of overdetermined systems of differential equations. Through the Cauchy problem, additional parameters are introduced, and from the definition of the integral, the equations defining the appearance of this integral immediately follow. Integrals can be used to reduce the order of the systems of differential equations, as well as to control the calculations of various practically relevant systems of equations, such as the Hamilton-Jacobi equations. They are used in various methods of finding solutions to differential equations.
Keywords:overdetermined systems of differential equations, PD equation systems of random order, integrals of PD equation systems, Cauchy problem.
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