Geodesic
Fundamental solution of initial-boundary value problem for fourth-order pseudoparabolic equations with nonsmooth coefficients
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 1, pp. 17-32 
I. G. Mamedov. Fundamental solution of initial-boundary value problem for fourth-order pseudoparabolic equations with nonsmooth coefficients. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 1, pp. 17-32. http://geodesic.mathdoc.fr/item/VMJ_2010_12_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the fundamental solution of initial-boundary value problem for pseudoparabolic equations with dominated derivatives of fourth order with nonsmooth coefficients is constructed.

[1] Yurchuk N. I., Baranovskaya S. N., Yashkin V. I., “O klassicheskikh i oslablennykh klassicheskikh resheniyakh giperbolicheskikh uravnenii”, Tez. dokl. mezhdunar. konf., posvyaschennoi 75-letiyu chl.-korr. RAN prof. L. D. Kudryavtseva, Moskva, 1998, 71

[2] Colton D., “Pseudoparabolic equations in one space variable”, J. Diff. equat., 12:3 (1972), 559–565 | DOI | MR | Zbl

[3] Shkhanukov M. Kh., Soldatov A. P., “Kraevye zadachi s obschim nelokalnym usloviem A. A. Samarskogo dlya psevdoparabolicheskikh uravnenii vysokogo poryadka”, Dokl. AN SSSR, 297:3 (1987), 547–552 | MR

[4] Zhegalov V. I., “Trekhmernyi analog zadachi Gursa”, Neklassicheskie uravneniya i uravneniya smeshannogo tipa, In-t matematiki SO AN SSSR, Novosibirsk, 1990, 94–98 | MR | Zbl

[5] Lerner M. E., “O kachestvennykh svoistvakh funktsii Rimana”, Differents. uravneniya, 27:12 (1991), 2106–2119 | MR

[6] Troitskaya S. D., “O pervoi kraevoi zadache dlya giperbolicheskogo uravneniya na ploskosti”, Mat. zametki, 65:2 (1999), 294–306 | DOI | MR | Zbl

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

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

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

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

[11] Vincenzo R. Di., Villani A., “Sopra in problema ai limiti per un'equatione lineare del terzo ordine di tipo iperbolico”, Esistenza, unicita e rappresentazione della solutione. Mathematice, 32:2 (1977), 211–238 | Zbl

[12] Mamedov I. G., “O novoi postanovke zadachi Gursa dlya odnogo nagruzhennogo volterro-giperbolicheskogo integro-differentsialnogo uravneniya chetvertogo poryadka”, Tez. dokl. mezhd. konferents. po matematike i mekhanike, posvyaschennoi 50-letiyu so dnya rozhdeniya chl.-korr. NANA, professora I. T. Mamedova, Baku, 2005, 123

[13] Mamedov I. G., “Generalization of multipoint boundary-value problems of Bitsadze–Samarski and Samarski–Ionkin type for fourth order loaded hyperbolic integro-differential equation and their operator generalization”, Proceedings of IMM of NAS of Azerbaijan, 23, 2005, 77–84 | MR | Zbl

[14] Amanov T. I., Prostranstva differentsiruemykh funktsii s dominiruyuschei smeshannoi proizvodnoi, Nauka, Alma-Ata, 1976, 171 pp. | MR

[15] Nikolskii C. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969, 455 pp. | MR | Zbl

[16] Lizorkin P. I., Nikolskii S. M., “Klassifikatsiya differentsiruemykh funktsii na osnove prostranstv s dominiruyuschei proizvodnoi”, Trudy MIAN SSSR, 77, 1965, 143–167 | MR | Zbl

[17] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975, 480 pp. | MR | Zbl

[18] Dzhabrailov A. Dzh., “O nekotorykh funktsionalnykh prostranstvakh. Pryamye i obratnye teoremy vlozheniya”, Dokl. AN SSSR, 159 (1964), 254–257 | MR | Zbl

[19] Akhiev S. S., “Ob obschem vide lineinykh ogranichennykh funktsionalov v odnom funktsionalnom prostranstve tipa S. L. Soboleva”, Dokl. AN. Azerb. SSR, 35:6 (1976), 3–7 | MR

[20] Nadzhafov A. M., “Ob integralnykh predstavleniyakh funktsii iz prostranstv s dominiruyuschei smeshannoi proizvodnoi”, Vestnik BGU. Cer. fiz.-mat. nauk, 3 (2005), 31–39 | MR

[21] Mamedov I. G., “Ob odnom razlozhenii dlya nepreryvnoi funktsii mnogikh peremennykh”, Vestnik BGU. Cer. fiz.-mat. nauk, 3 (1999), 144–152

[22] Mamedov I. G., “Zadacha Gursa novogo tipa dlya nagruzhennykh volterro-giperbolicheskikh integro-differentsialnykh vektornykh uravnenii chetvertogo poryadka s negladkimi matrichnymi koeffitsientami”, Izv. NAN Azerbaidzhana. Cer. FTMN, 26:2 (2006), 74–79 | MR