Boundary-value problems for a nonlinear hyperbolic equation with divergent part and Levy Laplacian

  • M. N. Feller УкрНИИ «Ресурс», Киев

Abstract

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 $U(0, x) = v_0, \;\;U(t, x) |_{\Gamma} = v_1, \;\; \lim_{||x||_H \rightarrow \infty} U(t, x) = v_2$ for the nonlinear hyperbolic equation $$\frac{\partial}{\partial t}\left[k(U(t,x))\frac{\partial U(t,x)}{\partial t}\right] = \Delta_L U(t,x)$$ with divergent part and infinite-dimensional Levy Laplacian $\Delta_L$.
Published
25.02.2012
How to Cite
FellerM. N. “Boundary-Value Problems for a Nonlinear Hyperbolic Equation With Divergent Part and Levy Laplacian”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 2, Feb. 2012, pp. 237-44, http://umj.imath.kiev.ua/index.php/umj/article/view/2570.
Section
Research articles