Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Khromov A. P. On Classic Solution of the Problem for a Homogeneous Wave Equation with Fixed End-Points and Zero Initial Velocity. Izv. Sarat. Univ. Math. Mech. Inform., 2019, vol. 19, iss. 3, pp. 280-288. DOI: 10.18500/1816-9791-2019-19-3-280-288

Published online: 
31.08.2019
Full text:
(downloads: 52)
Language: 
Russian
Heading: 
Article type: 
Article
UDC: 
517.96:517.984
DOI: 
10.18500/1816-9791-2019-19-3-280-288

On Classic Solution of the Problem for a Homogeneous Wave Equation with Fixed End-Points and Zero Initial Velocity

Autors: 
Khromov Avgust Petrovich, Saratov State University
Abstract: 

The paper gives necessary and sufficient conditions of classic solution for a homogeneous wave equation with a summable potential, fixed end-point, and zero initial velocity. With the use of Fourier method and Krylov method of improving series rate convergence an analogue of d’Alembert formula is derived in the form of exponentially convergent series. The paper essentially supports and extends the results of our work carried out in 2016. The suggested new method, based on the use of divergent (in Euler’s sense) series, is very economical in using well-known mathematical facts. It opens a perspective of considerable advancement in studying other boundary problems for partial differential equations.

References: 
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Received: 
24.04.2019