Mixed problem for a first-order partial differential equation with involution and periodic boundary conditions

The Fourier method is used to find a classical solution of the mixed problem for a first-order differential equation with involution and periodic boundary conditions. The application of the Fourier method is substantiated using refined asymptotic formulas obtained for the eigenvalues and eigenfuncti...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 54; no. 1; pp. 1 - 10
Main Author: Burlutskaya, M. Sh
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.01.2014
Springer Nature B.V
Subjects:
Asymptotic methods
Asymptotic properties
Boundary conditions
Computational mathematics
Computational Mathematics and Numerical Analysis
Differential equations
Eigenvalues
Fourier analysis
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Partial differential equations
Spectra
Studies
mixed problem for a first-order partial differential equation with involution
asymptotics of eigenvalues and eigenfunctions
classical solution
Fourier method
Dirac system
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:The Fourier method is used to find a classical solution of the mixed problem for a first-order differential equation with involution and periodic boundary conditions. The application of the Fourier method is substantiated using refined asymptotic formulas obtained for the eigenvalues and eigenfunctions of the corresponding spectral problem. The Fourier series representing the formal solution is transformed using certain techniques, and the possibility of its term-by-term differentiation is proved. Minimal requirements are imposed on the initial data of the problem.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542514010059