Boundary-value problems for a nonlinear hyperbolic equation with variable coefficients and the Lévy Laplacian.

For a nonlinear hyperbolic equation with variable coefficients and the infinite-dimensional Lévy Laplacian Δ, we present algorithms for the solution of the boundary-value problem U(0, x) = u, U( t, 0) = u and the exterior boundary-value problem U(0, x) = v, $$\left. {U(t,x)} \right|_{\Gamma = v_1 }$$, $$\lim _{\left\| x \right\|_{H \to \infty } } \left. {U(t,x) = v_2 } \right|$$ for the class of Shilov functions depending on the parameter t. [ABSTRACT FROM AUTHOR]