Geodesic
Boundary-Value Problems for a Nonlinear Hyperbolic Equation with Variable Coefficients and the L\'evy Laplacian
Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 440-449

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For a nonlinear hyperbolic equation with variable coefficients and the infinite-dimensional Lévy Laplacian $\Delta _L$, $$ \beta\biggl(\sqrt{2}\mspace{2mu}\|x\|_H \frac{\partial U(t,x)}{\partial t}\biggr) \frac{\partial^2U(t,x)}{\partial t^2} +\alpha(U(t,x)) \biggl[\frac{\partial U(t,x)}{\partial t}\biggr]^2 =\Delta_LU(t,x), $$ we present algorithms for the solution of the boundary-value problem $U(0,x)=u_0$, $U(t,0)=u_1$ and the exterior boundary-value problem $U(0,x)=v_0$, $U(t,x)|_\Gamma=v_1$, $\lim_{\|x\|_H\to\infty}U(t,x)=v_2$ for the class of Shilov functions depending on the parameter $t$.
Keywords: nonlinear hyperbolic equation, boundary-value problem, Lévy Laplacian, Shilov function, Hilbert space. 
@article{MZM_2014_96_3_a12,
     author = {M. N. Feller},
     title = {Boundary-Value {Problems} for a {Nonlinear} {Hyperbolic} {Equation} with {Variable} {Coefficients} and the {L\'evy} {Laplacian}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {440--449},
     publisher = {mathdoc},
     volume = {96},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a12/}
}
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M. N. Feller. Boundary-Value Problems for a Nonlinear Hyperbolic Equation with Variable Coefficients and the L\'evy Laplacian. Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 440-449. http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a12/