On a boundary value problem in a cylinder for a sixth-order pseudohyperbolic equation

The paper considers the first boundary value problem in a cylinder for one sixth-order equation not resolved with respect to the highest derivative. Equation under study is a strictly pseudohyperbolic with lower terms. In this work, the existence and uniqueness of a generalized solution to a boundary value problem in an anisotropic Sobolev space is proved, and estimates for the solution are obtained.

УДК 517.95

Keywords: pseudohyperbolic equation, boundary value problem, generalized solution, anisotropic Sobolev space, generalized Boussinesq equation.