Boundary-value problems for hyperbolic equations with constant coefficients

Abstract

By using a metric approach, we study the problem of well-posedness of boundary-value problems for hyperbolic equations of ordern $(n ≥ 2)$ with constant coefficients in a cylindrical domain. Conditions of existence and uniqueness of solutions are formulated in number-theoretic terms. We prove a metric theorem on lower estimates of small denominators that appear when constructing solutions.