Cite this article as:

Burlutskaya M. S., Khromov A. P. Mixed problem for simplest hyperbolic first order equations with involution . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 1, pp. 10-20. DOI: https://doi.org/10.18500/1816-9791-2014-14-1-10-20

Language: 
Russian
Heading: 
Mathematics
UDC: 
517.95+517.984

Mixed problem for simplest hyperbolic first order equations with involution

Authors: 
Burlutskaya Marija Shaukatovna, Voronezh State University, Voronezh State University, Russia, 394006, Voronezh, Universitetskaya pl., 1 , burlutskaya@math.vsu.ru, bmsh2001@mail.ru
Khromov Avgust Petrovich, Saratov State University 1, Saratov State University, Russia, 410012, Saratov, Astrahanskaya st., 83 , KhromovAP@info.sgu.ru
Abstract: 

In this paper investigates the mixed problem for the first order differential equation with involution at the potential and with periodic boundary conditions. Using the received refined asymptotic formulas for eigenvalues and eigenfunctions of the corresponding spectral problem, the application of the Fourier method is substantiated. We used techniques, which allow to avoid investigation of the uniform convergence of the series, obtained by term by term differentiation of formal solution on method of Fourier. This allows to get a classical solution with minimal requirements on the initial data of the problem. 

Key words: 
ixed problem, involution, Fourier method, classical solution, asymptotic form of eigenvalues and eigenfunctions, Dirac system.
DOI: 
https://doi.org/10.18500/1816-9791-2014-14-1-10-20
References
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