Consider the hyperbolic equation with variable coefficients Du(t, x) P(x) 012 = divx (p(x)gradzu) - q(x)u (t, x) in the domain Q = {(x, t) : xen CR",t >0} with initial conditions 1 (t, 1) 10 = 4(I), du (0.2) and Boundary conditions du a(r)u (t, x) + B(x) lan = 0(0.3) Functions p(x), q(r), p(r), o(x), B(x) are smooth enough (For example: p((x) E C' (0) , a, B, q, p E C (Q) Let p(x) > po > 0, p(x) 2 po > 0, q(x) 2 0, a(x) 20, B(x) 20, 03 +82 >0\f