Document Zbl 0842.35143

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Justification of the Fourier method for solving a boundary value problem in mathematical physics with random initial conditions. (English. Russian original) Zbl 0842.35143

Theory Probab. Math. Stat. 45, 121-127 (1992); translation from Teor. Veroyatn. Mat. Stat., Kiev 45, 127-135 (1991).

The author obtains sufficient conditions for the convergence of a random Fourier series to a solution of a boundary value problem for homogeneous hyperbolic equation in the norm of the Sobolev space \(W^1_2\). Also estimates of the rate of this convergence in \(L_2\) and \(W^1_2\) are obtained.

Reviewer: A.D.Borisenko (Kiev)

MSC:

35R60	PDEs with randomness, stochastic partial differential equations
42B99	Harmonic analysis in several variables
35L20	Initial-boundary value problems for second-order hyperbolic equations

Keywords:

random Fourier series; convergence

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