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For the following nonlinear hyperbolic equation with variable coefficients and the infinite-dimensional Lévy Laplacian Δ, formulas for the solution of the boundary-value problem and of the exterior boundary-value problem are obtained. [ABSTRACT FROM AUTHOR]

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]

We present solutions of the boundary-value problem and the external boundary-value problem for the nonlinear hyperbolic equation with infinite-dimensional Lévy Laplacian Δ: [ABSTRACT FROM AUTHOR]

We propose an algorithm for the solution of the boundary-value problem and the external boundary-value problem for the nonlinear hyperbolic equation with divergent part and infinite-dimensional Lévy Laplacian ∆. [ABSTRACT FROM AUTHOR]

We present the solutions of boundary-value and initial boundary-value problems for a nonlinear parabolic equation with Lévy Laplacian ∆ resolved with respect to the derivativein fundamental domains of a Hilbert space. [ABSTRACT FROM AUTHOR]

We present the solutions of the initial-value problem in the entire space and the solutions of the boundary-value and initial-boundary-value problems for the wave equationwith infinite-dimensional Lévy Laplacian Δ L in the class of Gâteaux functions. [ABSTRACT FROM AUTHOR]