The generalized homogenous thermoconvection problem of the non-compressible viscoelastic fluid
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 8 (2011), pp. 62-69
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The homogenous thermoconvection model of the non-compressible viscoelastic Kelvin–Voight fluid of the highest order is considered. The existence and uniqueness theorem of the solution which is a quasi-stationary semi-trajectory is proved in the frames of the Sobolev type equations theory. The description of the phase space is obtained.
Mots-clés : Sobolev type equations
Keywords: an incompressible viscoelastic fluid, phase space.
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O. P. Matveeva; T. G. Sukacheva. The generalized homogenous thermoconvection problem of the non-compressible viscoelastic fluid. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 8 (2011), pp. 62-69. http://geodesic.mathdoc.fr/item/VYURU_2011_8_a6/

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

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

[3] T. G. Sukacheva, O. P. Matveeva, “Ob odnorodnoi modeli termokonvektsii neszhimaemoi vyazkouprugoi zhidkosti Kelvina–Foigta nenulevogo poryadka”, Vestn. Samar. tekhn. un-ta. Ser. Fiziko-matematicheskie nauki, 2010, no. 5(21), 37–45 | MR

[4] G. A. Sviridyuk, V. E. Fedorov, Sobolev type equations and degenerate semigroups of operators, VSP, Utrecht–Boston, 2003, 179 pp. | MR | Zbl

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

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

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

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

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

[10] Yu. G. Borisovich, V. G. Zvyagin, Yu. I. Sapronov, “Nelineinye fredgolmovy otobrazheniya i teoriya Lere–Shaudera”, Uspekhi matem. nauk, 32:4 (1977), 3–54 | MR

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

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

[13] T. G. Sukacheva, “O razreshimosti nestatsionarnoi zadachi dinamiki neszhimaemoi vyazkouprugoi zhidkosti Kelvina–Foigta nenulevogo poryadka”, Izv. vuzov. Matem., 1998, no. 3 (430), 47–54

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

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