Geodesic
Boundary-Value Problems for a Nonlinear Hyperbolic Equation with Variable Coefficients and the L\'evy Laplacian.~II
Matematičeskie zametki, Tome 97 (2015) no. 6, pp. 917-924

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For the following nonlinear hyperbolic equation with variable coefficients and the infinite-dimensional Lévy Laplacian $\Delta_L$, \begin{align*} \biggl(\sqrt{2}\|x\|_H \frac{\partial U(t,x)}{\partial t} \ln\frac{1}{\sqrt{2}\|x\|_H (\partial U(t,x)/\partial t)}\biggr)^{-1} \frac{\partial^2U(t,x)}{\partial t^2} -\alpha(U(t,x)) \biggl[\frac{\partial U(t,x)}{\partial t}\biggr]^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. 
@article{MZM_2015_97_6_a8,
     author = {M. N. Feller},
     title = {Boundary-Value {Problems} for a {Nonlinear} {Hyperbolic} {Equation} with {Variable} {Coefficients} and the {L\'evy} {Laplacian.~II}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {917--924},
     publisher = {mathdoc},
     volume = {97},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_6_a8/}
}
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M. N. Feller. Boundary-Value Problems for a Nonlinear Hyperbolic Equation with Variable Coefficients and the L\'evy Laplacian.~II. Matematičeskie zametki, Tome 97 (2015) no. 6, pp. 917-924. http://geodesic.mathdoc.fr/item/MZM_2015_97_6_a8/