Some local and nonlocal boundary value problems for hyperbolic equations (in Russian)

Abstract

The paper deals with local and nonlocal boundary value problems for hyperbolic equations, which generalize the Darboux, Goursat and Cauchy problems. Under certain conditions on the given functions the correctness of these problems is proved, in other cases the uniqueness of the solution is proved and theorems of uniqueness of the solution in a more wide class of functions are stated. In the paper examples are given, showing the non-stability of the solution if some of the conditions on the boundary data are violated.