Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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Khromov A. P. Divergent series and generalized mixed problem for wave equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 3, pp. 351-358. DOI: 10.18500/1816-9791-2024-24-3-351-358, EDN: HWFUYG

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.08.2024
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Language: 
Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.927.96+517.984
DOI: 
10.18500/1816-9791-2024-24-3-351-358
EDN: 
HWFUYG

Divergent series and generalized mixed problem for wave equation

Autors: 
Khromov August Petrovich, Saratov State University
Abstract: 

Allowing the inversion of the operations of summation and integration for trigonometric Fourier series we present the solution by Fourier method of the generalized mixed problem for the homogeneous wave equation with zero initial velocity and fixed ends boundary conditions. The solution has the form of a series converging at an exponential rate. This series converges the classical solution if the latter equists. The results of the article reinforce the previously obtained results.

Key words: 
divergent series
wave equation
mixed problem
References: 
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Received: 
22.02.2024
Accepted: 
17.05.2024
Published: 
30.08.2024
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