Geodesic
A problem with analogue of the Frankl and mixing conditions for the Gellerstedt equation with singular coefficient
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2024), pp. 37-48 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the equation $ ({\rm sign} y)|y|^{m}u_{xx}+u_{yy}+\alpha_{_{0}}|y|^{(m-2)/2}u_{x}+(\beta_{0}/y)u_{y}=0, $, considered in some unbounded mixed domain, uniqueness and existence theorems for a solution to the problem with the missing shift condition on the boundary characteristics and an analogue of the Frankl type condition on the interval of degeneracy of the equation are proved.
Keywords: unbounded domain, missing shift condition, analogue of the Frankl condition, non-Fredholm operator, isolated first-order singularity, singular integral equation, Wiener–Hopf equation, index, unique solvability. 
@article{IVM_2024_6_a3,
     author = {D. M. Mirsaburova},
     title = {A problem with analogue of the {Frankl} and mixing conditions for the {Gellerstedt} equation with singular coefficient},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {37--48},
     year = {2024},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2024_6_a3/}
}
TY  - JOUR
AU  - D. M. Mirsaburova
TI  - A problem with analogue of the Frankl and mixing conditions for the Gellerstedt equation with singular coefficient
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2024
SP  - 37
EP  - 48
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IVM_2024_6_a3/
LA  - ru
ID  - IVM_2024_6_a3
ER  - 
%0 Journal Article
%A D. M. Mirsaburova
%T A problem with analogue of the Frankl and mixing conditions for the Gellerstedt equation with singular coefficient
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2024
%P 37-48
%N 6
%U http://geodesic.mathdoc.fr/item/IVM_2024_6_a3/
%G ru
%F IVM_2024_6_a3
D. M. Mirsaburova. A problem with analogue of the Frankl and mixing conditions for the Gellerstedt equation with singular coefficient. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2024), pp. 37-48. http://geodesic.mathdoc.fr/item/IVM_2024_6_a3/

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

[2] Bitsadze A.V., “K teorii uravnenii smeshannogo tipa, poryadok kotorykh vyrozhdaetsya vdol linii izmeneniya tipa”, Mekhanika sploshnoi sredy i rodstvennye problemy analiza, Nauka, M., 1972, 47–52

[3] Zhegalov V.I., “Kraevaya zadacha dlya uravneniya smeshannogo tipa s granichnymi usloviyami na perekhodnoi linii”, Uchen. zap. Kazansk. un-ta, 122, no. 3, 1962, 3–16 | Zbl

[4] Nakhushev A.M., “O nekotorykh kraevykh zadachakh dlya giperbolicheskikh uravnenii i uravnenii smeshannogo tipa”, Differents. uravneniya, 5:1 (1969), 44–59 | Zbl

[5] Trikomi F.D., O lineinykh uravneniyakh v chastnykh proizvodnykh vtorogo poryadka smeshannogo tipa, Gostekhizdat, M.-L., 1947

[6] Frankl F.I., “Obtekanie profilei potokom dozvukovoi skorosti so sverkh-zvukovoi zonoi, okanchivayusheisya pryamym skachkom uplotneniya”, Prikl. matem. i mekhan., 20:2 (1956), 196–202 | Zbl

[7] Devingtal Yu.V., “K voprosu o suschestvovanii i edinstvennosti resheniya zadachi Franklya”, Uspekhi matem. nauk, 14:1 (1959), 177–182 | MR | Zbl

[8] Lin Tszyan-bin, “O nekotorykh zadachakh Franklya”, Vestn. LGU. Ser. matem. mekhan. i astron., 3:13 (1961), 28–39 | Zbl

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

[10] Kapustin N.Yu., Sabitov K.B., “O reshenii odnoi problemy v teorii zadachi Franklya dlya uravnenii smeshannogo tipa”, Differents. uravneniya, 27:1 (1991), 60–68 | MR | Zbl

[11] Smirnov M.M., Uravneniya smeshannogo tipa, Vyssh. shk., M., 1985

[12] Mirsaburova Gulnora M., “Zadacha s nelokalnymi usloviyami na chastyakh granichnykh kharakteristik i na otrezke vyrozhdeniya dlya uravneniya Gellerstedta s singularnym koeffitsientom”, Izv. vuzov. Matem., 2020, no. 1, 64–83 | MR | Zbl

[13] Salakhitdinov M.S., Mirsaburov M., Nelokalnye zadachi dlya uravnenii smeshannogo tipa s singulyarnymi koeffitsientami, Universitet, Tashkent, 2005

[14] Babenko K.I., K teorii uravnenii smeshannogo tipa, Dokt. dis., MIAN, M., 1951

[15] Smirnov M.M., Uravneniya smeshannogo tipa, Nauka, M., 1970

[16] Volkodavov V.F., “O edinstvennosti resheniya zadachi $TN$ dlya odnogo uravneniya smeshannogo tipa”, Volzhsk. matem. sb., 9, Kuibyshevsk. gos. ped. in-ta, Kuibyshev, 1970, 55–65

[17] Bitsadze A.V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981 | MR

[18] Mirsaburova U.M., “Zadacha so smescheniem na vnutrennikh kharakteristikakh v neogranichennoi oblasti dlya uravneniya Gellerstedta s singulyarnym koeffitsientom”, Izv. vuzov. Matem., 2022, no. 9, 70–82 | MR | Zbl

[19] Gakhov F.D., Cherskii Yu.I., Uravneniya tipa svertki, Nauka, M., 1978 | MR

[20] Mirsaburov M., Khurramov N., “Zadacha s usloviem Bitsadze–Samarskogo na kharakteristikakh odnogo semeistva i obshimi usloviyami sopryazheniya na linii vyrozhdeniya dlya uravneniya Gellerstedta s singulyarnym koeffitsientom”, Differents. uravneniya, 56:8 (2020), 1073–1094 | DOI | Zbl