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

• Date: 2012
• Main Authors: Kovtun, I. I., Feller, M. N., Ковтун, И. И., Феллер, М. Н.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2012
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2675
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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}...