Geodesic
The Cauchy Problem for the Wave Equation with L\'evy Laplacian
Matematičeskie zametki, Tome 87 (2010) no. 6, pp. 803-813

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We present the solution of the Cauchy problem (the initial-value problem in the whole space) for the wave equation with infinite-dimensional Lévy Laplacian $\Delta _L$, $$ \frac{\partial^2 U(t,x)}{\partial t^2}=\Delta_LU(t,x) $$ in two function classes, the Shilov class and the Gâteaux class.
Keywords: wave equation, hyperbolic equation, Lévy Laplacian, Cauchy problem, Shilov function class, Hilbert space, variational derivative.
Mots-clés : Gâteaux function class 
@article{MZM_2010_87_6_a0,
     author = {S. A. Albeverio and Ya. I. Belopol'skaya and M. N. Feller},
     title = {The {Cauchy} {Problem} for the {Wave} {Equation} with {L\'evy} {Laplacian}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--813},
     publisher = {mathdoc},
     volume = {87},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_6_a0/}
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S. A. Albeverio; Ya. I. Belopol'skaya; M. N. Feller. The Cauchy Problem for the Wave Equation with L\'evy Laplacian. Matematičeskie zametki, Tome 87 (2010) no. 6, pp. 803-813. http://geodesic.mathdoc.fr/item/MZM_2010_87_6_a0/