DISSIPATIVITY OF BOUNDARY CONDITION IN A MIXED PROBLEM FOR THE THREE-DIMENSIONAL WAVE EQUATION

We consider a mixed problem for the real three-dimensional wave equation satisfying the uniform Lopatinskii condition. We describe all feasible ways of reduction of the problem to the mixed problem for the symmetric hyperbolic system with the dissipative boundary condition. These ways are patametrized by points of the upper part of a four-dimensional bodily cone of the second order. We characterize the cone location and its geometric parameters by means of the coefficients of the boundary condition in the problem under consideration.