Spline approximations of the solution of a~singular integro-differential equation

T. G. Sukacheva ; O. P. Matveeva

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2001), pp. 46-53.

Bibliographie

[1] Oskolkov A. P., “Nachalno-kraevye zadachi dlya uravnenii dvizheniya zhidkostei Kelvina–Foigta i zhidkostei Oldroita”, Tr. Matem. in-ta AN SSSR, 179, 1988, 126–164 | MR

[2] Karazeeva N. A., Kotsiolis A. A., Oskolkov A. P., Ob attraktorakh i dinamicheskikh sistemakh, porozhdennykh nachalno-kraevymi zadachami dlya uravnenii dvizheniya lineinykh vyazkouprugikh zhidkostei, Preprint LOMI R-10-88, 1988, 58 pp.

[3] Sviridyuk G. A., “Razreshimost zadachi termokonvektsii vyazkouprugoi neszhimaemoi zhidkosti”, Izv. vuzov. Matematika, 1990, no. 12, 65–70 | MR | Zbl

[4] Sviridyuk G. A., “K obschei teorii polugrupp operatorov”, UMN, 49:4 (1994), 47–74 | MR | Zbl

[5] Sviridyuk G. A., “Kvazistatsionarnye traektorii polulineinykh dinamicheskikh uravnenii tipa Soboleva”, Izv. RAN. Ser. matem., 57:3 (1993), 192–207 | MR | Zbl

[6] Sviridyuk G. A., Sukacheva T. G., “Fazovye prostranstva odnogo klassa operatornykh uravnenii”, Differents. uravneniya, 26:2 (1990), 250–258 | MR | Zbl

[7] Sviridyuk G. A., Sukacheva T. G., “Zadacha Koshi dlya odnogo klassa polulineinykh uravnenii tipa Soboleva”, Sib. matem. zhurn., 31:5 (1990), 109–119 | MR | Zbl

[8] Levine H. A., “Some nonexistence and instability theorems for solutions of formally parabolic equations of form $Du_t=-Au+F(u)$”, Arch. Rat. Mech. Anal., 51:5 (1973), 371–386 | DOI | MR | Zbl

[9] Borisovich Yu. G., Zvyagin V. G., Sapronov Yu. I., “Nelineinye fredgolmovy otobrazheniya i teoriya Lere-Shaudera”, UMN, 32:4 (1977), 3–54 | MR | Zbl

[10] Marsden Dzh., Mak-Kraken M., Bifurkatsiya rozhdeniya tsikla i ee prilozheniya, Mir, M., 1980, 368 pp. | MR | Zbl

[11] Bokareva T. A., Issledovanie fazovykh prostranstv uravnenii tipa Soboleva s otnositelno sektorialnymi operatorami, Diss. ...kand. fiz.-matem. nauk, Sankt-Peterburg, 1993, 107 pp.

[12] Sviridyuk G. A., “Ob odnoi modeli dinamiki slaboszhimaemoi vyazkouprugoi zhidkosti”, Izv. vuzov. Matematika, 1994, no. 1, 62–70 | MR | Zbl

[13] Sukacheva T. G., “Ob odnoi modeli dvizheniya neszhimaemoi vyazkouprugoi zhidkosti Kelvina–Foigta nenulevogo poryadka”, Differents. uravneniya, 33:4 (1997), 552–557 | MR | Zbl

[14] Sviridyuk G. A., “Polulineinye uravneniya tipa Soboleva s otnositelno ogranichennym operatorom”, DAN SSSR, 318:4 (1991), 828–831 | MR | Zbl

[15] Sviridyuk G. A., Sukacheva T. G., Dudko L. L., “Neobkhodimye i dostatochnye usloviya otnositelnoi $\sigma$-ogranichennosti lineinykh operatorov”, Dokl. RAN, 345:1 (1995), 25–27 | MR | Zbl

[16] Sviridyuk G. A., Sukacheva T. G., Dudko L. L., “Otnositelnaya $\sigma$-ogranichennost lineinykh operatorov”, Izv. vuzov. Matematika, 1997, no. 7, 68–73 | MR | Zbl

[17] Sviridyuk G. A., “Polulineinye uravneniya tipa Soboleva s otnositelno sektorialnymi operatorami”, Dokl. RAN, 329:3 (1993), 274–277 | Zbl

[18] Sviridyuk G. A., “Fazovye prostranstva polulineinykh uravnenii tipa Soboleva s otnositelno silno sektorialnym operatorom”, Algebra i analiz, 6:5 (1994), 252–272 | MR | Zbl

[19] Sviridyuk G. A., Fedorov V. E., “Analiticheskie polugruppy s yadrami i lineinye uravneniya tipa Soboleva”, Sib. matem. zhurn., 36:5 (1995), 1130–1145 | MR | Zbl

[20] Khenri D., Geometricheskaya teoriya polulineinykh parabolicheskikh uravnenii, Mir, M., 1985, 376 pp. | MR

[21] Sukacheva T. G., “O razreshimosti nestatsionarnoi zadachi dinamiki neszhimaemoi vyazkouprugoi zhidkosti Kelvina-Foigta nenulevogo poryadka”, Izv. vuzov. Matematika, 1998, no. 3, 47–54 | MR | Zbl