On Some Boundary Value Problems for a Class of Hyperbolic Systems of Second Order in Conic Domains

It can be easily verified that the system (1.1) by virtue of the condition (1.2) is hyperbolic. Let D be the conic domain {(x, t) ∈Rn+1 : |x|g(x/|x|) < t < +∞} lying in the half-space t > 0, and bounded by the conic manifold S= {(x, t) ∈Rn+1 : t = |x|g(x/|x|)}, where g is an entirely definite, positive, continuous, piecewise smooth function given on the unit sphere of the space Rn. For τ > 0, by Dτ := {(x, t) ∈Rn+1 : |x|g(x/|x|) < t < τ} we denote the domain lying in the half-space t > 0, bounded by the cone S and the hyperplane t = τ.