Geodesic
Substantiation of Fourier method in mixed problem with involution
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 3-12 
M. Sh. Burlutskaya; A. P. Khromov. Substantiation of Fourier method in mixed problem with involution. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 3-12. http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the mixed problem for the first order differential equation with involution is investigated. Using the received specified 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 transform a series representing the formal solution on Fourier method, and to prove the possibility of its term by term differentiation. At the same time on the initial problem data minimum requirements are imposed.

[1] Krylov A. N., O nekotorykh differentsialnykh uravneniyakh matematicheskoi fiziki, imeyuschikh prilozheniya v tekhnicheskikh voprosakh, L., 1950, 368 pp.

[2] Chernyatin V. A., Obosnovanie metoda Fure v smeshannoi zadache dlya uravnenii v chastnykh proizvodnykh, M., 1991, 112 pp. | MR | Zbl

[3] Khromov A. P., “Smeshannaya zadacha dlya differentsialnogo uravneniya s involyutsiei i potentsialom spetsialnogo vida”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 10:4 (2010), 17–22

[4] Burlutskaya M. Sh., Khromov A. P., “O klassicheskom reshenii smeshannoi zadachi dlya uravneniya pervogo poryadka s involyutsiei”, Vestn. Voronezh. gos. un-ta. Ser. Fizika. Matematika, 2010, no. 2, 26–33

[5] Burlutskaya M. Sh., Khromov A. P., “Klassicheskoe reshenie dlya smeshannoi zadachi s involyutsiei”, Dokl. RAN, 435:2 (2010), 151–154 | MR | Zbl

[6] Khromov A. P., “Ob asimptotike reshenii uravneniya Diraka”, Sovremennye metody teorii funktsii i smezhnye problemy, materialy Voronezh. zimnei mat. shk., Voronezh, 2011, 346–347

[7] Burlutskaya M. Sh., “Utochnennye asimptoticheskie formuly reshenii sistemy Diraka”, Sovremennye metody teorii funktsii i smezhnye problemy, materialy Voronezh. zimnei mat. shk., Voronezh, 2011, 53–54