Initial-boundary value problems for higher order linear hyperbolic equations with two independent variables were studied in  and , where necessary and sufficient conditions of solvability and unique solvability of well-posed cases, as well as in ill-posed cases, were established. In our research, we study the case with three independent variables. For that, the methods developed in  and  were modified.
Douglass, Andrew, "Initial-Boundary Value Problems for Higher Order Linear PDEs with Three Independent Variables" (2015). Mathematics and System Engineering Student Publications. 5.