Investigation of the nonlocal initial boundary value problems for some hyperbolic equations

Abstract

In the present article we are interested in the analysis of nonlocal initial boundary value problems for some medium oscillation equations. More precisely, we investigate di¤erent types of nonlocal problems for one-dimensional oscillation equations and prove existence and uniqueness theorems. In some cases algorithms for direct construction of the solution are given. We also consider nonlocal problem for multidimensional hyperbolic equation and prove the uniqueness theorem for the formulated initial boundary value problem applying the theory of characteristics under rather general assumptions.