On a Cauchy problem with periodic initial values
https://doi.org/10.22405/2226-8383-2021-22-5-16-24
Abstract
In the paper, the method of exponential sums is applied to the solution of partial differential equation. At the initial step, the authors decrease the dimension of the problem by separation of
variables. Thus the initial problem reduses to the system of the ordinary differential equations.
This allows one to use Fourier analysis.
About the Authors
Ludmila Gennad’evna Arkhipova
Lomonosov Moscow State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Vladimir Nikolaevich Chubarikov
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Miller W.,Jr. 1980. The method of trigonometric sums in the theory of numbers. 2nd Edition., correct.and supplement. — Moscow.: Fizmatlit. pp. 144.
2. Vinogradov I. M. 1976. Special variants of the trigonometrical sums method. — M.: Fizmatlit, pp. 144.
3. Courant R. 1964. Equations with partitial derivatives. — M.: Mir ,pp. 830.
4. Hua Loo-Keng. 1983. Selected Papers. — N.-Y.,Heidelberg, Berlin, pp.888.
5. Arkhipov G. I., 2013. Selected papers. — Orjol: Publ.House of the Orjol University, pp. 464.
6. Arkhipov G. I.„ Sadovnichii V. A., Chubarikov V. N. 2004. Lecture on mathematical analysis. 4th Ed., corr. — M.: Drofa. pp. 640.
Review
For citations:
Arkhipova L.G., Chubarikov V.N. On a Cauchy problem with periodic initial values. Chebyshevskii Sbornik. 2021;22(5):16-24. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-5-16-24
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