Approximation by parabolic systems of partial differential equations of higher order systems of quasilinear partial differential equations of the first order - Kazmerchuk, Anatolii (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2026)
In the theory of systems of quasilinear partial differential equations of the first order, the problem of justification of approximate methods for solving the Cauchy problem is important. In this work, the concept of a generalized solution of the Cauchy problem is introduced for systems of quasilinear partial differential equations of the first order. An analysis of the approximate method using a parabolic system of higher-order differential equations is also proposed. This approach allows us to understand how approximations work, which are an analogue of the Navier-Stokes system for the system of equations of hydromechanics.