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

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Abstract

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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Authors and Affiliations

  1. Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia

    M. Sh. Burlutskaya

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  1. M. Sh. Burlutskaya
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Correspondence to M. Sh. Burlutskaya.

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Original Russian Text © M.Sh. Burlutskaya, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 1, pp. 3–12.

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Burlutskaya, M.S. Mixed problem for a first-order partial differential equation with involution and periodic boundary conditions. Comput. Math. and Math. Phys. 54, 1–10 (2014). https://doi.org/10.1134/S0965542514010059

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  • DOI: https://doi.org/10.1134/S0965542514010059

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