Well-Posedness of a Local Boundary Value Problem in a Cylindrical Domain for Multidimensional Hyperbolic Equations with the Wave Operator

Resumo

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 Poincaré problems. We prove a criterion for the uniqueness of a regular solution. Bibliography: 17 titles.