Geodesic
On one mixed problem with involution
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 46-54.

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In this paper, we examine a mixed problem for an equation with an involutive deviation in the argument and periodic boundary conditions. Using the Fourier method, we obtain a classical solution to the problem with minimal requirements for the initial data of the problem. Also, we used some methods of improving the convergence of the series representing a formal solution.
Keywords: functional differential operator, involution, mixed problem, Fourier method. 
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D. V. Belova. On one mixed problem with involution. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 5, Tome 194 (2021), pp. 46-54. http://geodesic.mathdoc.fr/item/INTO_2021_194_a4/

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