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Mat. Zametki, 2015, Volume 97, Issue 6, Pages 917–924 (Mi mz10660)  

Boundary-Value Problems for a Nonlinear Hyperbolic Equation with Variable Coefficients and the Lévy Laplacian. II

M. N. Feller

Ukrainian Research Institute "Resource", Kiev

Abstract: For the following nonlinear hyperbolic equation with variable coefficients and the infinite-dimensional Lévy Laplacian $\Delta_L$,
\begin{align*} &(\sqrt{2}\|x\|_H \frac{\partial U(t,x)}{\partial t} \ln\frac{1}{\sqrt{2}\|x\|_H (\partial U(t,x)/\partial t)})^{-1} \frac{\partial^2U(t,x)}{\partial t^2} -\alpha(U(t,x)) [\frac{\partial U(t,x)}{\partial t}]^2
&\qquad =\Delta_LU(t,x), \end{align*}
formulas for the solution of the boundary-value problem
$$ U(0,x)=u_0,\qquad U(t,0)=u_1 $$
and of the exterior boundary-value problem
$$ U(0,x)=v_0,\qquad U(t,x)|_\Gamma=v_1,\qquad \lim_{\|x\|_H \to\infty}U(t,x)=v_2 $$
are obtained.

Keywords: nonlinear hyperbolic equation, Lévy Laplacian, boundary-value problem, exterior boundary-value problem, Shilov function class.

DOI: https://doi.org/10.4213/mzm10660

Full text: PDF file (444 kB)
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English version:
Mathematical Notes, 2015, 97:6, 930–936

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 07.08.2014

Citation: M. N. Feller, “Boundary-Value Problems for a Nonlinear Hyperbolic Equation with Variable Coefficients and the Lévy Laplacian. II”, Mat. Zametki, 97:6 (2015), 917–924; Math. Notes, 97:6 (2015), 930–936

Citation in format AMSBIB
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