Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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Khromov A. P., Burlutskaya M. S. Classical solution by the Fourier method of mixed problems with minimum requirements on the initial data. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 2, pp. 171-198. DOI: 10.18500/1816-9791-2014-14-2-171-198, EDN: SHHIEZ

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
09.06.2014
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Russian
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Mathematics
UDC: 
517.95+517.984
DOI: 
10.18500/1816-9791-2014-14-2-171-198
EDN: 
SHHIEZ

Classical solution by the Fourier method of mixed problems with minimum requirements on the initial data

Autors: 
Khromov August Petrovich, Saratov State University
Burlutskaya Marija Shaukatovna, Voronezh State University
Abstract: 

The article gives a new short proof the V. A. Chernyatin theorem about the classical solution of the Fourier method of the mixed problem for the wave equation with fixed ends with minimum requirements on the initial data. Next, a similar problem for the simplest functional differential equation of the first order with involution in the case of the fixed end is considered, and also obtained definitive results. These results are due to a significant use of ideas A. N. Krylova to accelerate the convergence of series, like Fourier series. The results for other similar mixed problems given without proof.

Key words: 
mixed problem
Fourier method
involution
classical solution
asymptotic form of eigenvalues and eigenfunctions
Dirac system
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Received: 
13.11.2014
Accepted: 
20.04.2014
Published: 
30.05.2014
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