On a solution of a boundary-value problem for a hyperbolic equation on a disk with random initial conditions
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.
KeywordsUniform Convergence Hyperbolic Equation Fourier Method Liouville Problem Random Initial Condition
- 2.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.Google Scholar
- 3.A. M. Samoilenko, S. A. Krivosheya, and N. A. Perestyuk, Differential Equations. Examples and Problems [in Ukrainian] Vyshcha Shkola, Kiev 1994.Google Scholar
- 4.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).Google Scholar
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