Geodesic
Research of the linearized Boussinesq system of equations by methods of theory of degenerate operator semigroups
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 11 (2009), pp. 62-69 
M. V. Plekhanova; A. F. Islamova. Research of the linearized Boussinesq system of equations by methods of theory of degenerate operator semigroups. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 11 (2009), pp. 62-69. http://geodesic.mathdoc.fr/item/VCHGU_2009_11_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Initial boundary value problem for the linearized Boussinesq system of equations is reduced to the the Cauchy problem for Sobolev type equation with strongly $(L,0)$-sectorial operator from the right and from the left.

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

[2] U. Yusupaliev, A. K. Maslov, S. A. Shuteev, “Teplovydelenie kak mekhanizm samopodderzhaniya zakruchennogo potoka v gaze”, Priklad. fizika, 2000, no. 1, 5–10

[3] G. A. Sviridyuk, V. E. Fedorov, “O edinitsakh analiticheskikh polugrupp operatorov s yadrami”, Sib. mat. zhurn., 39:3 (1998), 604–616 | MR

[4] V. E. Fedorov, “Golomorfnye razreshayuschie polugruppy uravnenii sobolevskogo tipa v lokalno vypuklykh prostranstvakh”, Mat. sb., 195:8 (2004), 131–160 | DOI | Zbl

[5] G. A. Sviridyuk, A. A. Efremov, “Optimalnoe upravlenie lineinymi uravneniyami tipa Soboleva s otnositelno p-sektorialnymi operatorami”, Differents. uravneniya, 31:11 (1995), 1912–1919 | MR | Zbl

[6] V. A. Solonnikov, “Otsenki tenzorov Grina dlya nekotorykh granichnykh zadach”, Dokl. AN SSSR, 130:5 (1960), 988–991 | MR | Zbl

[7] I. I. Vorovich, V. I. Yudovich, “Statsionarnye techeniya vyazkoi neszhimaemoi zhidkosti”, Mat. sb., 53:4 (1961), 393–428

[8] V. E. Fedorov, “Vyrozhdennye silno nepreryvnye polugruppy operatorov”, Algebra i analiz, 12:3 (2000), 173—200