Geodesic
Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 53-61.

Voir la notice de l'article provenant de la source Math-Net.Ru

For a mixed-type equation of the second kind with a singular coefficient with the use of spectral expansions, we establish a uniqueness criterion for solving the problem with incomplete boundary data. The solution is constructed in the form of the Fourier–Bessel sums. In substantiation of the uniform convergence we establish an estmate on separation from zero of small denominator with the corresponding asymptotic behavior that allowed to substantiate the convergence of the series in the class of regular solutions.
Keywords: mixed type equation, Keldysh problem, spectral method, uniqueness, Fourier–Bessel series, small denominators.
Mots-clés : singular coefficient 
@article{IVM_2017_8_a4,
     author = {R. M. Safina},
     title = {Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {53--61},
     publisher = {mathdoc},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_8_a4/}
}
TY  - JOUR
AU  - R. M. Safina
TI  - Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 53
EP  - 61
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_8_a4/
LA  - ru
ID  - IVM_2017_8_a4
ER  - 
%0 Journal Article
%A R. M. Safina
%T Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 53-61
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_8_a4/
%G ru
%F IVM_2017_8_a4
R. M. Safina. Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 53-61. http://geodesic.mathdoc.fr/item/IVM_2017_8_a4/

[1] Sokhadze R. S., “O pervoi kraevoi zadache dlya uravneniya smeshannogo tipa v pryamougolnike”, Differents. uravneniya, 19:1 (1983), 127–133

[2] Khachev M. M., Pervaya kraevaya zadacha dlya lineinykh uravnenii smeshannogo tipa, Izd. “Elbrus”, Nalchik, 1998

[3] Sabitov K. B., Suleimanova A. Kh., “Zadacha Dirikhle dlya uravneniya smeshannogo tipa vtorogo roda v pryamougolnoi oblasti”, Izv. vuzov. Matem., 2007, no. 4, 45–53 | Zbl

[4] Sabitov K. B., Suleimanova A. Kh., “Zadacha Dirikhle dlya uravneniya smeshannogo tipa s kharakteristicheskim vyrozhdeniem v pryamougolnoi oblasti”, Izv. vuzov. Matem., 2009, no. 11, 43–52 | Zbl

[5] Khairullin R. S., “K zadache Dirikhle dlya uravneniya smeshannogo tipa vtorogo roda s silnym vyrozhdeniem”, Differents. uravneniya, 49:4 (2013), 528–534 | Zbl

[6] Arnold V. I., “Malye znamenateli i problemy ustoichivosti dvizheniya v klassicheskoi i nebesnoi mekhanike”, UMN, 18:6(114) (1963), 91–192 | MR | Zbl

[7] Lomov S. A., Lomov I. S., Osnovy matematicheskoi teorii pogranichnogo sloya, MGU, M., 2011

[8] Safina R. M., “Zadacha Keldysha dlya uravneniya Pulkina v pryamougolnoi oblasti”, Vestn. Samarsk. gos. un-ta. Estestvennonauchn. ser., 2015, no. 3, 53–64

[9] Safina R. M., “Zadacha Keldysha dlya uravneniya smeshannogo tipa vtorogo roda s operatorom Besselya”, Differents. uravneniya, 51:10 (2015), 1354–1366 | DOI | Zbl

[10] Keldysh M. V., “O nekotorykh sluchayakh vyrozhdeniya uravnenii ellipticheskogo tipa na granitse oblasti”, DAN SSSR, 77:2 (1951), 181–183 | Zbl

[11] Pulkin S. P., “O edinstvennosti resheniya singulyarnoi zadachi Gellerstedta”, Izv. vuzov. Matem., 1960, no. 6, 214–225 | Zbl

[12] Sabitov K. B., K teorii uravnenii smeshannogo tipa, Fizmatlit, M., 2014

[13] Sabitov K. B., Vagapova E. V., “Zadacha Dirikhle dlya uravneniya smeshannogo tipa s dvumya liniyami vyrozhdeniya v pryamougolnoi oblasti”, Differents. uravneniya, 49:1 (2013), 68–78 | MR | Zbl

[14] Olver F., Vvedenie v asimptoticheskie metody i spetsialnye funktsii, Mir, M., 1986

[15] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, v. II, Nauka, M., 1966 | MR