Boundary-value problems for a nonlinear hyperbolic equation with divergent part and Levy Laplacian - Feller, M. N. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We propose an algorithm for the solution of the boundary-value problem U(0,x) = u_0, U(t, 0) = u_1 and the external boundary-value problem U(0, x) = v_0, U(t, x) |_Γ = v_1, _||x||_H → ∞ U(t, x) = v_2 for the nonlinear hyperbolic equation t[k(U(t,x))U(t,x)t] = Δ_L U(t,x) with divergent part and infinite-dimensional Levy Laplacian Δ_L.