A Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Data on the Entire Boundary of a Domain

Abstract

In a domain that is the Cartesian product of a segment and a p-dimensional torus, we investigate a boundary-value problem for weakly nonlinear hyperbolic equations of higher order. For almost all (with respect to Lebesgue measure) parameters of the domain, we establish conditions for the existence of a unique solution of the problem.