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

  • I. I. Kovtun Нац. ун-т биоресурсов и природопользования Украины, Киев
  • M. N. Feller УкрНИИ «Ресурс», Киев

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 $∆_L$.
Published
25.11.2012
How to Cite
KovtunI. I., and FellerM. N. “Boundary-Value Problems for a Nonlinear Hyperbolic Equation With Levy Laplaciana”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 11, Nov. 2012, pp. 1492-9, http://umj.imath.kiev.ua/index.php/umj/article/view/2675.
Section
Research articles