On well-posedness of a mixed problem for the wave equation

We consider a mixed problem in a quarter-space for the wave equation with two spatial variables. The boundary condition is a linear combination of the first derivatives.
We study boundary conditions under which the mixed problem satisfies the Lopatinskii condition. The established criterion is constructive. Namely, we verify that a second order polynomial is Hurwitzian. Coefficients of the polynomial are defined explicitly by the coefficients of the boundary condition of the mixed problem.
We prove well-posedness of the problems satisfying the Lopatinskii condition by means of constructing a dissipative energy integral allowing us to obtain easily a priori estimate. To construct the dissipative energy integral we solve a system of linear algebraic equations.