Boundary-value problems for a nonlinear hyperbolic equation with variable coefficients and the L,vy Laplacian

For a nonlinear hyperbolic equation with variable coefficients and the infinite-dimensional Levy Laplacian Delta(L), beta(root 2 parallel to x parallel to(H) partial derivative U(t,x)/partial derivative t)partial derivative U-2(t,x)/partial derivative t(2) + alpha(U(t,x))[partial derivative U(t,x)/partial derivative t](2) = Delta U-L(t,x), we present algorithms for the solution of the boundary-value problem U(0, x) = u(0), U(t, 0) = u(1) and the exterior boundary-value problem U(0, x) = v(0), U(t,x)vertical bar Gamma = v(1), lim(parallel to x parallel to H ->infinity)U(t,x) = v(2) for the class of Shilov functions depending on the parameter t.