About an initial boundary problem for a degenerate higher even order partial differential equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 155-170.

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For one degenerate differential equation in partial derivatives of high even order with operator The initial boundary value problem is formulated in the rectangle and the existence, uniqueness and stability of the solution of the problem under study are proved.
Keywords: degenerate partial differential equation initial-boundary value problem, spectral problem, the existence, uniqueness and stability of the solution, the method of separation of variables. .
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A. K. Urinov; M. S. Azizov. About an initial boundary problem for a degenerate higher even order partial differential equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 155-170. http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a12/

[1] A. N. Tikhonov, A. A. Samarskii, Uravneniya matematicheskoi fiziki, Nauka, M., 1972 | MR

[2] B. G. Korenev, Voprosy rascheta balok i plit na uprugom osnovanii, Stroiizdat, M., 1954

[3] E. V. Makhover, “Izgib plastinki peremennoi tolschiny s ostrym kraem”, Uch. zap. LGP im. Gertsena, 17:2 (1957), 28–39

[4] E. V. Makhover, “O spektre sobstvennykh chastot plastinki s ostrym kraem”, Uch. zap. LGP im. Gertsena, 197 (1958), 113–118

[5] B. A. Bubnov, V. N. Vragov, “K teorii korrektnykh kraevykh zadach dlya nekotorykh klassov ultragi perbolicheskikh uravnenii”, Dokl. AN SSSR, 264:4 (1982), 795–800 | MR | Zbl

[6] I. E. Egorov, “Razreshimost odnoi kraevoi zadachi dlya uravneniya smeshannogo tipa vysokogo poryadka”, Differents. uravneniya, 23:9 (1987), 1560–1567 | MR | Zbl

[7] I. E. Fedorov I. E. Egorov, “O pervoi kraevoi zadache dlya odnogo uravneniya smeshannogo tipa vysokogo poryadka”, Metody prikl. matematiki i mat. fiziki, YaF SO AN SSSR, Yakutsk, 1987, 8–14 | MR

[8] I. E. Egorov, “Kraevaya zadacha dlya odnogo uravneniya vysokogo poryadka s menyayuschimsya napravleniem vremeni”, Dokl. AN SSSR, 303:6 (1988), 1301–1304

[9] A. I. Kozhanov, “O kraevykh zadachakh dlya nekotorykh klassov uravnenii vysokogo poryadka, nerazre shennykh otnositelno starshei proizvodnoi”, Sib. mat. zhurn., 35:2 (1994), 359–376 | MR | Zbl

[10] A. I. Kozhanov, N. R. Pinigina, “Kraevye zadachi dlya nekotorykh klassov uravnenii sostavnogo tipa vysokogo poryadka”, Sib. elektron. mat. izv, 12 (2015), 842–853 | Zbl

[11] R. R. Ashurov, A. T. Muhiddinova, “Initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary elliptic differential operator”, Lobachevskii J. Math., 42:3 (2021), 517–525 | DOI | MR | Zbl

[12] D. Amanov, “About correctness of boundary value problems for an equation of even order”, Uzbek Math. J., 2011, no. 4, 20–35 | MR

[13] D. Amanov, A. Ashuraliyev, “Well-posedness of boundary value problems for partial differential equations of even order”, First Internat. Conf. Anal. Appl. Math., 2012, 3–7 | MR

[14] A. K. Urinov, M. S. Azizov, “Nachalno-granichnaya zadacha dlya uravneniya v chastnykh proizvodnykh vysshego chetnogo poryadka s operatorom Besselya”, Vestn. Samar. gos. tekhn. un-ta. Ser. Fiz. mat. nauki, 26:2 (2022), 273–292 | DOI | Zbl

[15] A. K. Urinov, M. S. Azizov, “O razreshimosti nelokalnykh nachalno-granichnykh zadach dlya odnogo differentsialnogo uravneniya v chastnykh proizvodnykh vysokogo chetnogo poryadka”, Vestnyu Udmuryu un-ta. Matematika. Mekhanika. Kompyuternye nauki, 32:2 (2022), 240–255 | MR | Zbl

[16] M. S. Azizov, “Ob odnoi nachalno-granichnoi zadache dlya uravneniya v chastnykh proizvodnykh vysshego chetnogo poryadka s operatorom Besselya”, Byull. In-ta matematiki AN Respubliki Uz., 5:1 (2022), 14–24 | MR

[17] M. S. Azizov, “Ob odnoi nelokalnoi nachalno-granichnoi zadache dlya uravneniya v chastnykh proizvodnykh vysokogo chetnogo poryadka v pryamougolnike”, Byull. In-ta matematiki AN Respubliki Uz., 5:5 (2022), 112–133

[18] I. A. Kipriyanov, Singulyarnye ellipticheskie kraevye zadachi, Nauka, M., 1997 | MR

[19] K. B. Sabitov, “Zadacha Dirikhle dlya uravnenii s chastnymi proizvodnymi vysokikh poryadkov”, Mat. zametki, 97:2 (2015), 262–276 | DOI | Zbl

[20] B. Yu. Irgashev, “O spektralnoi zadache dlya odnogo uravneniya vysokogo chetnogo poryadka”, Izv. vuzov. Matematika, 2016, no. 7, 44–54 | MR | Zbl

[21] Yu. P. Apakov, B. Yu. Irgashev, “Kraevaya zadacha dlya vyrozhdayuschegosya uravneniya vysokogo nechetnogo poryadka”, Ukrain. mat. zhurn., 66:10 (2014), 1348–1331

[22] K. B. Sabitov, O. V. Fadeeva, “Nachalno-granichnaya zadacha dlya uravneniya vynuzhdennykh kolebanii konsolnoi balki”, Vestn. Samar. gos. un-ta. Ser. Fiz. mat. nauki, 25:1 (2021), 51–66 | DOI | Zbl

[23] K. B. Baikuziev, B. S. Kalanov, “O razreshimosti smeshannoi zadachi dlya uravneniya vysshego poryadka, vyrozhdayuschegosya na granitse oblasti”, Kraevye zadachi dlya differentsialnykh uravnenii, 2 (1972), 40–54 | MR

[24] K. B. Baikuziev, B. S. Kalanov, “O razreshimosti smeshannoi zadachi dlya uravneniya vysshego poryadka, vyrozhdayuschegosya na granitse oblasti”, Kraevye zadachi dlya differentsialnykh uravnenii, 3 (1973), 65–73 | MR | Zbl

[25] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. I, Nauka, M., 1965 | MR

[26] M. A. Naimark, Lineinye differentsialnye operatory, Nauka, M., 1969

[27] S. G. Mikhlin, Lektsii po lineinym integralnym uravneniyam, Fizmatlit, M., 1959

[28] Dzh. N. Vatson, Teorii besselevykh funktsii, Izd-vo inostr. lit-ry, M., 1949