Boundary-value problems for a nonlinear hyperbolic equation with divergent part and Levy Laplacian
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 $$\frac{\partial}...
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| Date: | 2012 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2570 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We propose an algorithm for the solution of the boundary-value problem $U(0,x) = u_0,\;\; U(t, 0) = u_1$ and the external
boundary-value problem $U(0, x) = v_0, \;\;U(t, x) |_{\Gamma} = v_1, \;\; \lim_{||x||_H \rightarrow \infty} U(t, x) = v_2$
for the nonlinear hyperbolic equation
$$\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 $\Delta_L$. |
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