2018
Том 70
№ 9

# Boundary-value problems for a nonlinear hyperbolic equation with Levy Laplaciana

Abstract

We present solutions of the boundary-value problem $U(0, x) = u_0, \;U(t, 0) = u_1$, and the external boundary-value problem $U(0, x) = v_0,\; U(t, x)|_{Γ} = v_1,\; \lim_{||x||_H→∞} U(t, x) = v_2$ for the nonlinear hyperbolic equation $$\frac{∂^2U(t, x)}{∂t^2} + α(U(t, x)) \left[\frac{∂U(t, x)}{∂t}\right]^2 = ∆_LU(t, x)$$ with infinite-dimensional Levy Laplacian $∆_L$.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 11, pp 1688-1697.

Citation Example: Feller M. N., Kovtun I. I. Boundary-value problems for a nonlinear hyperbolic equation with Levy Laplaciana // Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1492-1499.

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