Unique solvability of initial boundary-value problems for hyperbolic systems in cylinders whose base is a cusp domain

We study initial boundary-value problems for hyperbolic systems of divergence form of arbitrary order in cylinders whose base is a cusp domain. Our main results are to prove the existence, uniqueness and the smoothness with respect to time variable of generalized solutions of these problems by using the method which we will denote as "approximating boundary method".