Boundary problems for a special class of degenerate hyperbolic equations

We study the solvability of new boundary problems for a special class of degenerate second-order hyperbolic equations. These problems have two features. The first is the presence of two variables in the equation, each of which can be considered as a time variable. This means that problems with fundamentally different boundary conditions can be correct for these equations. The second feature is the presence of degeneracy. This means that the boundary problems formulation can change depending on the nature of degeneration. For the problems under study,we prove theorems of existence and uniqueness for regular solutions are proven, i.e. solutions that have all generalized according to Sobolev derivatives included in the equation.