Geodesic
The problem with missing condition of shift for singular coefficiensy Gellerstedt equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2018), pp. 52-63.

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

For Gellerstedt equation with singular coefficient we prove theorems of uniqueness and existence of solution to the problem with the missing condition of shift on the boundary characteristics and Frankl type condition on degeneration segment of the equation.
Keywords: missing condition of shift, Frankl type condition, Tricomi non-standard singular integral equation, Wiener–Hopf equation, index. 
@article{IVM_2018_5_a6,
     author = {M. Mirsaburov},
     title = {The problem with missing condition of shift for singular coefficiensy {Gellerstedt} equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {52--63},
     publisher = {mathdoc},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_5_a6/}
}
TY  - JOUR
AU  - M. Mirsaburov
TI  - The problem with missing condition of shift for singular coefficiensy Gellerstedt equation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 52
EP  - 63
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_5_a6/
LA  - ru
ID  - IVM_2018_5_a6
ER  - 
%0 Journal Article
%A M. Mirsaburov
%T The problem with missing condition of shift for singular coefficiensy Gellerstedt equation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 52-63
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2018_5_a6/
%G ru
%F IVM_2018_5_a6
M. Mirsaburov. The problem with missing condition of shift for singular coefficiensy Gellerstedt equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2018), pp. 52-63. http://geodesic.mathdoc.fr/item/IVM_2018_5_a6/

[1] Zhegalov V. I., “Kraevaya zadacha dlya uravneniya smeshannogo tipa s granichnymi usloviyami na perekhodnoi linii”, Uchen. zap. Kazansk. un-ta, 122:3 (1962), 3–16

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

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

[4] Frankl F. I., “Obtekanie profilei gazom s mestnoi sverkhzvukovoi zonoi, okanchivayuscheisya pryamym skachkom uplotneniya”, PMM, 20:2 (1956), 196–202

[5] Devingtal Yu. V., “O suschestvovanii i edinstvennosti resheniya odnoi zadachi F. I. Franklya”, Izv. vuzov. Matem., 1958, no. 2, 39–51

[6] Lin Tszyan-bin, “O nekotorykh zadachakh Franklya”, Vestn. LGU. Matem., mekhan. i astronomiya, 3:13 (1961), 28–39

[7] Salakhitdinov M. S., Mirsaburov M., “Zadacha s nelokalnym granichnym usloviem na kharakteristike dlya odnogo klassa uravnenii smeshannogo tipa”, Matem. zametki, 86:5 (2009), 748–760 | DOI | MR

[8] Babenko K. I., K teorii uravnenii smeshannogo tipa, Diss. ... dokt. fiz-matem. nauk (biblioteka matem. in-ta im. V. A. Steklova RAN), 1952

[9] Salakhitdinov M. S., Mirsaburov M., Nelokalnye zadachi dlya uravnenii smeshannogo tipa s singulyarnymi koeffitsientami, “Univ.”, “Yangiyo'l poligraf servis”, Tashkent, 2005

[10] Smirnov M. M., Uravneniya smeshannogo tipa, Vyssh. shkola, M., 1985

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

[12] Polosin A. A., “Ob odnoznachnoi razreshimosti zadachi Trikomi dlya spetsialnoi oblasti”, Differents. uravneniya, 32:3 (1996), 394–401

[13] Mirsaburov M., “Kraevaya zadacha dlya odnogo klassa uravnenii smeshannogo tipa s usloviem Bitsadze–Samarskogo na parallelnykh kharakteristikakh”, Differents. uravneniya, 37:9 (2001), 1281–1284 | MR

[14] Mirsaburov M., Chorieva S. T., “Ob odnoi zadache so smescheniem dlya vyrozhdayuschegosya uravneniya smeshannogo tipa”, Izv. vuzov. Matem., 2015, no. 4, 46–54

[15] Soldatov A. P., “K nëterovskoi teorii operatorov. Odnomernye singulyarnye integralnye operatory obschego vida”, Differents. uravneniya, 14:4 (1978), 706–718

[16] Duduchava R. V., Integralnye uravneniya svertki s razryvnymi predsimvolami, singulyarnye integralnye uravneniya s nepodvizhnymi osobennostyami i ikh prilozheniya k zadacham mekhaniki, Tr. Tbilissk. matem. in-ta, Tbilisi, 1979

[17] Mikhlin S. G., “Ob integralnom uravnenii F. Tricomi”, DAN SSSR, 59:6 (1948), 1053–1056

[18] Gakhov F. D., Cherskii Yu. N., Uravneniya tipa svertki, Nauka, M., 1978