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This article is cited in 11 scientific papers (total in 11 papers)
Mathematics
Mixed problem for simplest hyperbolic first order equations with involution
M. Sh. Burlutskayaa, A. P. Khromovb a Voronezh State University, 1, Universitetskaya pl., 394006, Voronezh, Russia
b Saratov State University, 83, Astrahanskaya str., 410012, Saratov, Russia
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:
mixed problem, involution, Fourier method, classical solution, asymptotic form of eigenvalues and eigenfunctions, Dirac system.
Citation:
M. Sh. Burlutskaya, A. P. Khromov, “Mixed problem for simplest hyperbolic first order equations with involution”, Izv. Saratov Univ. Math. Mech. Inform., 14:1 (2014), 10–20
Linking options:
https://www.mathnet.ru/eng/isu479 https://www.mathnet.ru/eng/isu/v14/i1/p10
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