Geodesic
On a nonclassical interpretation of the four-dimensional Goursat problem for one hyberbolic equation
Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 4, pp. 59-66 
I. G. Mamedov. On a nonclassical interpretation of the four-dimensional Goursat problem for one hyberbolic equation. Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 4, pp. 59-66. http://geodesic.mathdoc.fr/item/VMJ_2015_17_4_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A homeomorphism between certain pairs of Banach space is revealed in the study of the four-dimensional Goursat problem for one differential equation with leading partial derivative of the sixth order $D_1D_2D_3^2D_4^2$ with discontinuous coefficients ($L_p$-coefficients) by reducing this problem to an equivalent integral equation.

[1] Zhegalov V. I., Sevastyanov V. A., “Zadacha Gursa v chetyrekhmernom prostranstve”, Dif. uravneniya, 32:10 (1996), 1429–1430 | MR | Zbl

[2] Zhegalov V. I., Mironov A. N., Differentsialnye uravneniya so starshimi chastnymi proizvodnymi, Kazanskoe mat. obschestvo, Kazan, 2001, 226 pp.

[3] Mironov A. N., “K zadache Koshi v chetyrekhmernom prostranstve”, Dif. uravneniya, 40:6 (2004), 844–847 | MR | Zbl

[4] Mironov A. N., “K metodu Rimana resheniya odnoi smeshannoi zadachi”, Vestn. Sam. gos. tekhn. un-ta. Ser. fiz.-mat. nauki, 2007, no. 2(15), 27–32 | DOI

[5] Koscheeva O. A., “O postroenii funktsii Rimana dlya uravneniya Bianki v $n$-mernom prostranstve”, Izv. vuzov. Matematika, 2008, no. 9, 40–46 | MR | Zbl

[6] Utkina E. A., “Ob odnoi kraevoi zadache so smescheniyami v chetyrekhmernom prostranstve”, Izv. vuzov. Matematika, 2009, no. 4, 50–55 | MR | Zbl

[7] Mironov A. N., “O postroenii funktsii Rimana dlya odnogo uravneniya so starshei chastnoi proizvodnoi pyatogo poryadka”, Dif. uravneniya, 46:2 (2010), 266–272 | MR | Zbl

[8] Dzhokhadze O. M., “O trekhmernoi obobschennoi zadache Gursa dlya uravneniya tretego poryadka i svyazannye s nei obschie dvumernye integralnye uravneniya Volterry pervogo roda”, Dif. uravneniya, 42:3 (2006), 385–394 | MR | Zbl

[9] Midodashvili B., “Generalized Goursat problem for a spatial fourth order hyperbolic equation with dominated low terms”, Proceedings of A. Razmadze Math. Institute, 138 (2005), 43–54 | MR | Zbl

[10] Berezin A. V., Vorontsov A. S., Markov M. B., Plyuschenkov B. D., “O vyvode i reshenii uravnenii Maksvella v zadachakh s zadannym volnovym frontom”, Mat. modelirovanie, 18:4 (2006), 43–60 | MR | Zbl

[11] Zhegalov V. I., Utkina E. A., “Ob odnom psevdoparabolicheskom uravnenii tretego poryadka”, Izv. vuzov. Matematika, 1999, no. 10, 73–76 | MR | Zbl

[12] Mamedov I. G., “Fundamentalnoe reshenie zadachi Koshi, svyazannoi s psevdoparabolicheskim uravneniem chetvertogo poryadka”, Zhurn. vychislitelnoi matematiki i mat. fiziki, 49:1 (2009), 99–110 | MR | Zbl

[13] Kozhanov A. I., “Ob odnoi nelokalnoi kraevoi zadache s peremennymi koeffitsientami dlya uravnenii teploprovodnosti i Allera”, Dif. uravneniya, 40:6 (2004), 763–764 | MR

[14] Vodakhova V. A., “Kraevaya zadacha s nelokalnym usloviem A. M. Nakhusheva dlya odnogo psevdoparabolicheskogo uravneniya vlagoperenosa”, Dif. uravneniya, 18:2 (1982), 280–285 | MR | Zbl

[15] Shkhanukov M. Kh., “O nekotorykh kraevykh zadachakh dlya uravneniya tretego poryadka, voznikayuschikh pri modelirovanii filtratsii zhidkosti v poristykh sredakh”, Dif. uravneniya, 18:4 (1982), 689–699 | MR | Zbl

[16] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995, 304 pp.

[17] Mamedov I. G., “Usloviya optimalnosti nekotorykh protsessov, opisyvaemykh psevdoparabolicheskim uravneniem pri nelokalnykh kraevykh usloviyakh”, Mat. i kompyuternoe modelirovanie. Ser. fiz.-mat. nauki, 2008, no. 1, 133–141

[18] Chernov A. V., “O totalnom sokhranenii globalnoi razreshimosti zadachi Gursa dlya upravlyaemogo polulineinogo psevdoparabolicheskogo uravneniya”, Vladikavk. mat. zhurn., 16:3 (2014), 55–63 | Zbl

[19] Mamedov I. G., “Formula integrirovaniya po chastyam neklassicheskogo tipa pri issledovanii zadachi Gursa dlya odnogo psevdoparabolicheskogo uravneniya”, Vladikavk. mat. zhurn., 13:4 (2011), 40–51 | MR | Zbl

[20] Mamedov I. G., “Nelokalnaya kombinirovannaya zadacha tipa Bitsadze–Samarskogo i Samarskogo–Ionkina dlya sistemy psevdoparabolicheskikh uravnenii”, Vladikavk. mat. zhurn., 16:1 (2014), 30–41 | Zbl

[21] Mamedov I. G., “O neklassicheskoi traktovke zadachi Dirikhle dlya odnogo psevdoparabolicheskogo uravneniya chetvertogo poryadka”, Dif. uravneniya, 50:3 (2014), 417–420 | DOI | Zbl

[22] Akhiev S. S., “Fundamentalnye resheniya nekotorykh lokalnykh i nelokalnykh kraevykh zadach i ikh predstavleniya”, Dokl. AN SSSR, 271:2 (1983), 265–269 | MR | Zbl

[23] Akhiev S. S., “Funktsiya Rimana uravneniya s dominiruyuschei smeshannoi proizvodnoi proizvolnogo poryadka”, Dokl. AN SSSR, 283:5 (1985), 783–787 | MR | Zbl

[24] Mamedov I. G., “Ob odnoi zadache Gursa v prostranstve Soboleva”, Izv. vuzov. Matematika, 2011, no. 2, 54–64 | MR | Zbl

[25] Mamedov I. G., “Fundamentalnoe reshenie nachalno-kraevoi zadachi dlya psevdoparabolicheskogo uravneniya chetvertogo poryadka s negladkimi koeffitsientami”, Vladikavk. mat. zhurn., 12:1 (2010), 17–32 | MR | Zbl