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This article is cited in 4 scientific papers (total in 4 papers)
The Cauchy Problem for the Wave Equation with Lévy Laplacian
S. A. Albeverioa, Ya. I. Belopol'skayab, M. N. Fellerc a University of Bonn, Institute for Applied Mathematics
b St. Petersburg State University of Architecture and Civil Engineering
c Ukranian Institune of Wood Machining
Abstract:
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, Gâteaux function class, Hilbert space, variational derivative.
Received: 12.11.2009
Citation:
S. A. Albeverio, Ya. I. Belopol'skaya, M. N. Feller, “The Cauchy Problem for the Wave Equation with Lévy Laplacian”, Mat. Zametki, 87:6 (2010), 803–813; Math. Notes, 87:6 (2010), 787–796
Linking options:
https://www.mathnet.ru/eng/mzm4744https://doi.org/10.4213/mzm4744 https://www.mathnet.ru/eng/mzm/v87/i6/p803
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Abstract page: | 511 | Full-text PDF : | 195 | References: | 52 | First page: | 21 |
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