Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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

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Mixed problem for simplest hyperbolic first order equations with involution

Burlutskaya Marija Shaukatovna, Voronezh State University, Russia
Khromov Avgust Petrovich, Saratov State University

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. 

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