An identification problem of source function for one semievolutionary system
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 4, pp. 487-499.

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An identification problem of source function for the semievolutionary system of two partial differential equations, one of which is parabolic, and the second – elliptic are investigated. The Cauchy problem and the first boundary-value problem are considered. Initial problems are approximated by problems in which the elliptic equation is replaced with the parabolic equation containing the small parameter $\varepsilon>0$ at a derivative with respect to time.
Keywords: partial differential equations, boundary-value problems, approximation, small parameter
Mots-clés : convergence.
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Yuri Ya. Belov. An identification problem of source function for one semievolutionary system. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 4, pp. 487-499. http://geodesic.mathdoc.fr/item/JSFU_2010_3_4_a5/

[1] A. P. Oskolkov, “Ob odnoi kvazilineinoi parabolicheskoi sisteme s malym parametrom, approksimiruyuschei sistemu uravnenii Nave–Stoksa”, Zapiski nauchnykh seminarov LOMI ANSSSR, 21, 1971, 79–103 | MR | Zbl

[2] P. E. Sobolevskii, V. V. Vasilev, “Ob odnoi $\varepsilon$-approksimatsii uravnenii Nave–Stoksa”, Chislennye metody mekhaniki sploshnoi sredy (Novosibirsk), 9:5 (1978), 115–139 | MR

[3] Yu. Ya. Belov, “Teoremy odnoznachnoi razreshimosti i approksimatsii nekotorykh kraevykh zadach dlya sistem uravnenii, opisyvayuschikh techenie okeana”, Sib. matem. zhurn., 20:6 (1979), 1206–1225 | MR | Zbl

[4] A. V. Kazhikhov, Izbrannye trudy. Matematicheskaya gidrodinamika, Izd-vo In-ta gidrodinamiki im. M. A. Lavrenteva SO RAN, Novosibirsk, 2008

[5] S. N. Antontsev, A. V. Kazhikhov, V. N. Monakhov, Kraevye zadachi mekhaniki neodnorodnykh zhidkostei, Novosibirsk, 1983 | MR

[6] Zh.-L. Lions, Nekotorye metody resheniya nelineinykh kraevykh zadach, Moskva, 1972

[7] Yu. Ya. Belov, Inverse Problems for Partial Differential Equations, VSP, Utrecht–Boston–Köln–Tokyo, 2002 | MR | Zbl

[8] P. Yu. Vyacheslavova, R. V. Sorokin, “Zadacha identifikatsii koeffitsientov pri mladshikh chlenakh v sisteme sostavnogo tipa”, Zhurnal SFU. Matematika i fizika, 2:3 (2009), 288–297

[9] R. V. Sorokin, T. N. Shipina, “O razreshimosti odnoi obratnoi zadachi dlya sistemy sostavnogo tipa”, Vychislitelnye tekhnologii, 8:3 (2003), 139–146

[10] A. I. Prilepko, D. G. Orlovsky, I. A. Vasin, Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekkar, Inc., New York, 1999 | MR

[11] N. N. Yanenko, Metod drobnykh shagov resheniya mnogomernykh zadach matematicheskoi fiziki, Nauka, Novosibirsk, 1967 | Zbl

[12] Yu. Ya. Belov, S. A. Kantor, Metod slaboi approksimatsii, KrasGU, Krasnoyarsk, 1999