S. A. Albeverio, Ya. I. Belopol'skaya, M. N. Feller, “The Cauchy Problem for the Wave Equation with Lévy Laplacian”, Mat. Zametki, 2010, Volume 87, Issue 6,Pages <nobr>803

This article is cited in 4 papers

The Cauchy Problem for the Wave Equation with Lévy Laplacian

S. A. Albeverio^a, Ya. I. Belopol'skaya^b, M. N. Feller^c

^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.

UDC: 517.958+517.98

Received: 12.11.2009

DOI: 10.4213/mzm4744