Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Kurdyumov V. P., Khromov A. P., Khalova V. A. Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity and a Summable Potential. Izv. Sarat. Univ. Math. Mech. Inform., 2020, vol. 20, iss. 4, pp. 444-456. DOI: 10.18500/1816-9791-2020-20-4-444-456

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.11.2020
Full text:
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Language: 
Russian
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Article type: 
Article
UDC: 
519.633
DOI: 
10.18500/1816-9791-2020-20-4-444-456

Mixed Problem for a Homogeneous Wave Equation with a Nonzero Initial Velocity and a Summable Potential

Autors: 
Kurdyumov Vitalii Pavlovich, Saratov State University
Khromov Avgust Petrovich, Saratov State University
Khalova Victoria Anatol'evna, Saratov State University
Abstract: 

For a mixed problem defined by a wave equation with a summable potential equal-order boundary conditions with a derivative and a zero initial position, the properties of the formal solution by the Fourier method are investigated depending on the smoothness of the initial velocity u′t(x, 0) = ψ(x). The research is based on the idea of A. N. Krylov on accelerating the convergence of Fourier series and on the method of contour integrating the resolvent of the operator of the corresponding spectral problem. The classical solution is obtained for ψ(x) ∈ W1p (1 < p ≤ 2), and it is also shown that if ψ(x) ∈ Lp[0, 1] (1 ≤ p ≤ 2), the formal solution is a generalized solution of the mixed problem.

References: 
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Received: 
11.06.2019
Accepted: 
28.06.2020
Published: 
30.11.2020