Abstract
We establish conditions under which a solution of a boundary-value problem for a hyperbolic equation on a disk with random initial conditions can be represented as a series uniformly convergent with probability one.
References
E. Barrasa de la Krus and Yu. V. Kozachenko, “Boundary-value problem for equations of mathematical physics with strictly Orlich random conditions,” Rand. Oper. Stochast. Equat., 3, No. 3, 201–220 (1995).
V. V. Buldygin and Yu. V. Kozachenko, “On the applicability of the Fourier method for the solution of problems with random boundary conditions,” in: Random Processes in Problems of Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1979), pp. 4–35.
A. M. Samoilenko, S. A. Krivosheya, and N. A. Perestyuk, Differential Equations. Examples and Problems [in Ukrainian] Vyshcha Shkola, Kiev 1994.
Yu. V. Kozachenko, “Conditions for the uniform convergence of Gauss series and trigonometric series close to them in the Luxemburg norm,” Teor. Ver. Mat. Stat., No. 28, 59–70 (1983).
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Oliinyk, A.O. On a solution of a boundary-value problem for a hyperbolic equation on a disk with random initial conditions. Ukr Math J 52, 470–478 (2000). https://doi.org/10.1007/BF02513141
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DOI: https://doi.org/10.1007/BF02513141