One boundary value problem for a pseudohyperbolic equation in a quarter-space

An initial-boundary value problem for a pseudohyperbolic equation in a quarter-space is studied in this article. This equation belongs to a class of partial differential equations not solvable with respect to the highest-order time-derivative. We obtain sufficient conditions for the right-hand side of the given equation under which the initial-boundary value problem is solvable in Sobolev spaces with an exponential weight.

УДК 517.954

Keywords: pseudohyperbolic equation, initial-boundary value problem, anisotropic Sobolev space.