Geodesic
Boundary value problem for a fourth-order equation of parabolic-hyperbolic type with multiple characteristics, whose slopes are greater than one
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2022), pp. 3-14.

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

In this paper, we set and study a boundary value problem for a fourth-order equation of parabolic-hyperbolic type with multiple characteristics, the slope of the first-order operator of which is greater than one, in a pentagonal domain. The unique solvability of the problem is proved by the method of direct composition of the solution.
Keywords: differential and integral equations, continuation method, boundary value problem, parabolic-hyperbolic equation, unique solvability.
Mots-clés : solution composition method 
@article{IVM_2022_4_a0,
     author = {Yu. P. Apakov and S. M. Mamajanov},
     title = {Boundary value problem for a fourth-order equation of parabolic-hyperbolic type with multiple characteristics, whose slopes are greater than one},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--14},
     publisher = {mathdoc},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_4_a0/}
}
TY  - JOUR
AU  - Yu. P. Apakov
AU  - S. M. Mamajanov
TI  - Boundary value problem for a fourth-order equation of parabolic-hyperbolic type with multiple characteristics, whose slopes are greater than one
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2022
SP  - 3
EP  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2022_4_a0/
LA  - ru
ID  - IVM_2022_4_a0
ER  - 
%0 Journal Article
%A Yu. P. Apakov
%A S. M. Mamajanov
%T Boundary value problem for a fourth-order equation of parabolic-hyperbolic type with multiple characteristics, whose slopes are greater than one
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2022
%P 3-14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2022_4_a0/
%G ru
%F IVM_2022_4_a0
Yu. P. Apakov; S. M. Mamajanov. Boundary value problem for a fourth-order equation of parabolic-hyperbolic type with multiple characteristics, whose slopes are greater than one. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2022), pp. 3-14. http://geodesic.mathdoc.fr/item/IVM_2022_4_a0/

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

[2] Gellerstedt S., Sur un probleme aux limites pour une équation linéaire aux dérivées partielles du second ordre de tipe mixte, Uppsala, 1935

[3] Bitsadze A. V., Uravneniya smeshannogo tipa, Izd-vo Akad. nauk SSSR, M., 1959 | MR

[4] Babenko K. I., K teorii uravnenii smeshannogo tipa, Avtoref. dis. na soisk. uchen. step. dokt. fiz.-matem. nauk, AN SSSR, M., 1952

[5] Karol I. L., “Ob odnoi kraevoi zadache dlya uravneniya smeshannogo elliptiko-giperbolicheskogo tipa”, DAN SSSR, 88:2 (1953), 197–200 | MR | Zbl

[6] Frankl F. I., “O zadachakh Chaplygina dlya smeshannykh do- i sverkhzvukovykh techenii”, Izv. AN SSSR, 9:2 (1945), 121–143 | Zbl

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

[8] Salakhitdinov M. S., Uravneniya smeshanno-sostavnogo tipa, Fan, Tashkent, 1974 | MR

[9] Gelfand I. M., “Nekotorye voprosy analiza i differentsialnykh uravnenii”, UMN, 14:3(87) (1959), 3–19 | Zbl

[10] Struchina G. M., “Zadacha o sopryazhenii dvukh uravnenii”, Inzhenerno-fiz. zhurn., 4:11 (1961), 99–104

[11] Uflyand Ya. S., “K voprosu o rasprostranenii kolebanii v sostavnykh elektricheskikh liniyakh”, Inzhenerno-fiz. zhurn., 7:1 (1964), 89–92

[12] Gaiduk S. I., Ivanov A. V., “Ob odnoi zadache na sopryazhenie uravnenii parabolicheskogo i giperbolicheskogo tipov”, DAN BSSR, 8:9 (1964), 560–563 | Zbl

[13] Gaiduk S. I., “Primenenie metoda konturnogo integrala k resheniyu odnoi zadachi na sopryazhenie uravnenii parabolicheskogo i giperbolicheskogo tipov”, Differents. uravneniya, 1:10 (1965), 1366–1382 | MR | Zbl

[14] Ladyzhenskaya O. A., Stupyalis L., “Ob uravneniyakh smeshannogo tipa”, Vestn. LGU, ser. matem., mekhan. i astr., 19:4 (1965), 38–46 | Zbl

[15] Akilov Zh. A., Nestatsionarnye dvizheniya vyazkouprugikh zhidkostei, Fan, Tashkent, 1982

[16] Apakov Yu. P., “Trekhmernyi analog zadachi Trikomi dlya parabolo-giperbolicheskogo uravneniya”, Sib. zhurn. industr. matem., 14:2 (2011), 34–44 | MR | Zbl

[17] Dzhuraev T. D., Kraevye zadachi dlya uravnenii smeshannogo i smeshanno-sostavnogo tipov, Fan, Tashkent, 1979 | MR

[18] Dzhuraev T. D., Sopuev A., Mamazhanov M., Kraevye zadachi dlya uravnenii parabolo-giperbolicheskogo tipa, Fan, Tashkent, 1986 | MR

[19] Dzhuraev T. D., Mamazhanov M., “Kraevye zadachi dlya odnogo klassa uravnenii chetvertogo poryadka smeshannogo tipa”, Differents. uravneniya, 22:1 (1986), 25–31 | MR | Zbl

[20] Sopuev A., Babaev S., Bekmamatov Z. M., “Rivisiting the Mixed Problem for Equations of Compound and Hyperbolic Types of Order Four”, Growth Poles of the Global economy: Emergence, Changes and Future Perspectives, Lect. Notes in Network and Syst., 73, 2020, 725–736 | DOI | Zbl

[21] Turbin M. V., “Issledovanie nachalno-kraevoi zadachi dlya modeli dvizheniya zhidkosti Gershel-Balkli”, Vest. Voronezh. gos. un-ta. Ser. Fiz. Matem., 2 (2013), 246–257 | Zbl

[22] Uizem Dzh., Lineinye i nelineinye volny, Mir, M., 1977

[23] Shabrov S. A., “Ob otsenkakh funktsii vliyaniya odnoi matematicheskoi modeli chetvertogo poryadka”, Vest. Voronezh. gos. un-ta. Ser. Fiz. Matem., 2 (2015), 168–179 | Zbl

[24] Benney D. J., Luke J. C., “On the interactions of permanent waves of finite amplitude”, J. Math. Phys., 43 (1964), 309–313 | DOI | MR | Zbl

[25] Sabitov K. B., “Kolebaniya balki s zadelannymi kontsami”, Vestn. Samarsk. gos. tekhn. un-ta. Ser. Fiz.-matem. nauki, 19:2 (2015), 311–324 | Zbl

[26] Amanov D., Murzambetov M. B., “Kraevaya zadacha dlya uravneniya chetvertogo poryadka s mladshim chlenom”, Vestn. Udmurtsk. un-ta. Matem. Mekhan. Kompyut. nauki, 1 (2013), 3–10 | Zbl

[27] Amanov D., “Razreshimost i volterovost kraevykh zadach dlya uravnenii chetvertogo poryadka”, DAN RUz, 1 (2011), 3–6

[28] Amanov D., Klichev A., “Kraevaya zadacha dlya uravneniya smeshannogo tipa chetvertogo poryadka v pryamougolnoi oblasti”, Byull. in-ta matem. AN RUz, 2 (2018), 1–8

[29] Yuldashev T. K., “Obratnaya zadacha dlya nelineinogo integro-differentsialnogo uravneniya Fredgolma chetvertogo poryadka s vyrozhdennymi yadrom”, Vestn. Samarsk. gos. tekh. un-ta. Ser. Fiz.-Matem. nauki, 19:4 (2015), 736–749 | Zbl

[30] Yuldashev T. K., “Nelokalnaya smeshannaya zadacha dlya integro-differentsialnogo uravneniya tipa Bussineska s vyrozhdennym yadrom”, Ukr. matem. zhurn., 68:8 (2016), 1115–1131

[31] Yuldashev T. K., “Ob odnoi kraevoi zadache dlya integro-differentsialnogo uravneniya v chastnykh proizvodnykh chetvertogo poryadka s vyrozhdennymi yadrom”, Geometriya i mekhanika, Itogi nauki i tekhniki. Sovremen. matem. i ee prilozh. Temat. obz., 145, 2018, 95–109 | MR

[32] Yuldashev T. K., “O razreshimosti odnoi kraevoi zadachi dlya differentsialnogo uravneniya tipa Bussineska”, Differents. uravneniya, 54:10 (2018), 1411–1419 | Zbl

[33] Pulkina L. S. Beylin A. B., “Nonlocal Approach to Problems on Longitudinal Vibrations in a Short Bar”, Electronic J. Diff. Equat., 2019:29 (2019), 1–9 | MR

[34] Asanova A. T. Tokmurzin Zh. S., “Ob odnom podkhode k resheniyu nachalno-kraevoi zadachi dlya sistemy giperbolicheskikh uravnenii chetvertogo poryadka”, Matem. zametki, 108:1 (2020), 3–16 | MR | Zbl

[35] Mamazhanov M., Mamazhanov S. M., “Postanovka i metod issledovaniya nekotorykh kraevykh zadach dlya odnogo klassa uravnenii chetvertogo poryadka parabolo-giperbolicheskogo tipa”, Vestn. KRAUNTs Fiz.-matem. nauki, 1:8 (2014), 14–19 | MR