Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Gurevich A. P., Kurdyumov V. P., Khromov A. P. Justification of Fourier Method in a Mixed Problem for Wave Equation with Non-zero Velocity. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 1, pp. 13-28. DOI: 10.18500/1816-9791-2016-16-1-13-29, EDN: VUSODD

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.03.2016
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Russian
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UDC: 
517.95;517.984
EDN: 
VUSODD

Justification of Fourier Method in a Mixed Problem for Wave Equation with Non-zero Velocity

Autors: 
Gurevich Alexandr Petrovich, Saratov State University
Kurdyumov Vitalii Pavlovich, Saratov State University
Khromov August Petrovich, Saratov State University
Abstract: 

In the paper, using contour integration of the resolvent of the corresponding spectral problem operator, justification of Fourier method in two mixed problems for wave equation with trivial initial function and non-zero velocity is given. The boundary conditions of these problems, together with fixed endpoint conditions, embrace all cases of mixed problems with the same initial conditions for which the corresponding spectral operators in Fourier method have regular boundary conditions. The problems are considered under minimal requirements on initial data. A. N. Krylov’s idea of accelerating Fourier series convergence is essentially employed.

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Received: 
19.11.2015
Accepted: 
27.02.2016
Published: 
31.03.2016