Investigation of the nonlocal initial boundary value problems for some hyperbolic equations (Q1348159)

This paper deals with nonlocal initial-boundary value problems for several classes of medium oscillation equations. The nonlocal conditions can be nonlinear, discrete and integral. In Theorems 2.1, 2.2 uniqueness results for nonlocal initial-boundary value problems to hyperbolic equations in the multidimensional case are proved. Nonlinear nonlocal problems for the string equation and for the telegraph equation are investigated in \S 3 and \S 4 of the paper under consideration and existence and uniqueness theorems for classical solutions are shown. In some cases algorithms for direct construction of the corresponding solutions are given.