Justification of an averaging scheme for hyperbolic systems with fast and slow variables. The mixed problem (Q579521)

This paper is concerned with a hyperbolic system which is averaged with respect to time. Actually, the author extends the well-known averaging method of N. N. Bogoljubov in the theory of ordinary differential equations to partial ones. An initial boundary value problem for a hyperbolic system of equations with small parameter \(\epsilon\) is considered. The right-hand sides of those are averaged with respect to time. A theorem is proved about proximity of solutions of the given and averaged hyperbolic systems. The proximity time-interval is directly proportional to \(\epsilon^{1/2}\). 6 references reflect the stated problem.