WELL-POSEDNESS OF A LOCAL BOUNDARY VALUE PROBLEM IN A CYLINDRICAL DOMAIN FOR MULTIDIMENSIONAL HYPERBOLIC EQUATIONS WITH THE WAVE OPERATOR

摘要

We establish the unique solvability of a local boundary value problem in a cylindrical domain for multi-dimensional hyperbolic equations with the wave operator. This problem is a generalization of the Dirichlet and Poincare problems. We prove a criterion for the uniqueness of a regular solution. Bibliography: 17 titles.