Geodesic
On the solvability of a boundary-value problem for a third-order differential equation with multiple characteristics
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 24-34.

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

In this paper, we discuss the unique solvability of a boundary-value problem for an inhomogeneous third-order partial differential equation with multiple characteristics. Using the Green function, we is construct a solution of this boundary-value problem in the explicit form.
Keywords: partial differential equation, third-order equation, equation with multiple characteristics, unique solvability, boundary-value problem. 
@article{INTO_2022_210_a3,
     author = {Yu. P. Apakov and T. K. Yuldashev and A. Kh. Zhuraev},
     title = {On the solvability of a boundary-value problem for a third-order differential equation with multiple characteristics},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {24--34},
     publisher = {mathdoc},
     volume = {210},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_210_a3/}
}
TY  - JOUR
AU  - Yu. P. Apakov
AU  - T. K. Yuldashev
AU  - A. Kh. Zhuraev
TI  - On the solvability of a boundary-value problem for a third-order differential equation with multiple characteristics
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 24
EP  - 34
VL  - 210
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_210_a3/
LA  - ru
ID  - INTO_2022_210_a3
ER  - 
%0 Journal Article
%A Yu. P. Apakov
%A T. K. Yuldashev
%A A. Kh. Zhuraev
%T On the solvability of a boundary-value problem for a third-order differential equation with multiple characteristics
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 24-34
%V 210
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_210_a3/
%G ru
%F INTO_2022_210_a3
Yu. P. Apakov; T. K. Yuldashev; A. Kh. Zhuraev. On the solvability of a boundary-value problem for a third-order differential equation with multiple characteristics. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 24-34. http://geodesic.mathdoc.fr/item/INTO_2022_210_a3/

[1] Abdinazarov S., “Ob odnom uravnenii tretego poryadka”, Izv. AN UzSSR. Ser. fiz.-mat. nauk., 1986, no. 3, 21–27

[2] Abdinazarov S., Sobirov Z. A., “Ob odnoi zadache dlya smeshannogo uravneniya vysokogo nechetnogo poryadka s kratnymi kharakteristikami”, Uzbek. mat. zh., 2003, no. 2, 3–8

[3] Apakov Yu. P., “Reshenie kraevykh zadach dlya uravneniya tretego poryadka s kratnymi kharakteristikami metodom razdeleniya peremennykh”, Uzbek. mat. zh., 2007, no. 1, 14–23 | MR | Zbl

[4] Apakov Yu. P., K teorii uravnenii tretego poryadka s kratnymi kharakteristikami, Fan va texnologiya, Tashkent, 2019

[5] Balkizov Zh. A., Kadzakov A. Kh., “O predstavlenii resheniya kraevoi zadachi dlya neodnorodnogo uravneniya tretego poryadka s kratnymi kharakteristikami”, Izv. Kabardino-Balkar. nauch. tsentra RAN., 2010, no. 4, 64–69

[6] Diesperov V. N., “O funktsii Grina linearizovannogo vyazkogo transzvukovogo uravneniya.”, Zh. vychisl. mat. mat. fiz., 12:5 (1972), 1265–1279 | MR | Zbl

[7] Dzhuraev T. D., Apakov Yu. P., “Ob avtomodelnom reshenii odnogo uravneniya tretego poryadka s kratnymi kharakteristikami”, Vestn. Samar. tekhn. un-ta. Ser. Fiz.-mat. nauki., 2007, no. 2 (15), 18–26 | Zbl

[8] Dzhuraev T. D., Apakov Yu. P., “K teorii uravneniya tretego poryadka s kratnymi kharakteristikami, soderzhaschego vtoruyu proizvodnuyu po vremeni”, Ukr. mat. zh., 62:1 (2010), 40–51 | Zbl

[9] Irgashev Yu., Apakov Yu. P., “Pervaya kraevaya zadacha dlya uravneniya tretego poryadka psevdoellipticheskogo tipa”, Uzbek. mat. zh., 2006, no. 2, 44–51 | MR

[10] Kozhanov A. I., Lukina G. A., “Prostranstvenno-nelokalnye zadachi s integralnymi usloviyami dlya differentsialnykh uravnenii tretego poryadka”, Differ. uravn., 53:7 (2017), 906–917

[11] Lukina G. A., “Kraevye zadachi s integralnymi granichnymi usloviyami dlya linearizovannogo uravneniya Kortevega—de Friza”, Vestn. Yuzhno-Ural. un-ta. Ser. Mat. model. program., 2011, no. 17 (234), 52–61 | Zbl

[12] Ryzhov O. S., “Asimptoticheskaya kartina obtekaniya tel vrascheniya zvukovym potokom vyazkogo i teploprovodyaschego gaza”, Prikl. mat. mekh., 2:6 (1952), 1004–1014

[13] Sabitov K. B., “Zadacha Dirikhle dlya uravnenie smeshannogo tipa tretego poryadka”, Dokl. RAN., 427:5 (2009), 593–596 | Zbl

[14] Shubin V. V., “Kraevye zadachi dlya uravnenii tretego poryadka s razryvnym koeffitsientom”, Vestn. NGU. Ser. Mat. mekh. inform., 12:1 (2012), 126–138 | Zbl

[15] Yuldashev T. K., “Obratnaya zadacha dlya odnogo integro-differentsialnogo uravneniya Fredgolma v chastnykh proizvodnykh tretego poryadka”, Vestn. Samar. tekhn. un-ta. Ser. Fiz.-mat. nauki., 2014, no. 1 (34), 56–65 | Zbl

[16] Yuldashev T. K., “Obratnaya zadacha dlya integro-differentsialnogo uravneniya Fredgolma tretego poryadka s vyrozhdennym yadrom”, Vladikavkaz. mat. zh., 18:2 (2016), 76–85 | MR | Zbl

[17] Yuldashev T. K., “Ob odnom integro-differentsialnom uravnenii Fredgolma v chastnykh proizvodnykh tretego poryadka”, Izv. vuzov. Mat., 2015, no. 9, 74–79 | Zbl

[18] Yuldashev T. K., “Smeshannaya zadacha dlya psevdoparabolicheskogo integro-differentsialnogo uravneniya s vyrozhdeniem yadra”, Differ. uravn., 53:1 (2017), 101–110 | Zbl

[19] Yuldashev T. K., “Nelokalnaya kraevaya zadacha dlya neodnorodnogo psevdoparabolicheskogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom”, Vestn. Volgograd. gos. un-ta. Ser. 1. Mat. Fiz., 2017, no. 1 (38), 42–54

[20] Ashyraliev A., Aggez N., Hezenci F., “Boundary-value problem for a third-order partal differential equation”, AIP Conf. Proc., 1470:1 (2012), 130–133 | DOI

[21] Bendjajazia N., Guezane-Lokoudi A., Khaldi R., “On third-order boundary-value problems with multiple characteristics”, Differ. Equations Dynam. Systems., https://doi.org/10.1007/s12591-019-00507-6

[22] Block H., “Sur les équations linéaires aux dérivées parielles à caratéristiques multiples. Note 1”, Ark. Mat. Astron. Fys., 7:13 (1912), 1–34

[23] Block H., “Sur les équations linéaires aux dérivées parielles à caratéristiques multiples. Note 2”, Ark. Mat. Astron. Fys., 7:21 (1912), 1–30

[24] Block H., “Sur les équations linéaires aux dérivées parielles à caratéristiques multiples. Note 3”, Ark. Mat. Astron. Fys., 8:23 (1912-1913), 1–51

[25] Cattabriga L., “Potenziali di linea e di dominio per equazioni non paraboliche in due variabili a caratteristiche multiple”, Rend. Semin. Mat. Univ. Padava., 1961, no. 31, 1–45 | MR | Zbl

[26] Del Vicchio E., “Sulle equazioni”, Mem. R. Accad. Sci. Ser. 2., 66 (1915), 1–41 | Zbl

[27] Del Vicchio E., “Sur deux problemes d’integration pour les equazios paraboliques”, Ark. For Mat. Astr. Fys., 11 (1916), 32–43

[28] Yuldashev T. K., Islomov B. I., Alikulov E. K., “Boundary-value problems for loaded third-order parabolic-hyperbolic equations in infinite three-dimensional domains”, Lobachevskii J. Math., 41:5 (2020), 926–944 | DOI | MR | Zbl