An identification problem of source function in the Burgers-type equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 497-506.

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An identification problem of source function in the Burgers-type equation is considered. Given problem is investigated in Cauchy and boundary-value cases. Sufficient conditions for existence and uniqueness of solution are obtained.
Keywords: inverse problem, Burgers' equation, boundary-value problem, approximation.
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Yuri Ya. Belov; Kirill V. Korshun. An identification problem of source function in the Burgers-type equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 497-506. http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a6/

[1] I. M. Burgers, “A mathematical model illustrating the theory of turbulence”, Advances of mechanics, 1 (1948), 171–199 | DOI | MR

[2] E. Hopf, “The partial differential equation $u_t+uu_x=\mu u_{xx}$”, Comm. Pure Appl. Math., 3:3 (1950), 201–230 | DOI | MR | Zbl

[3] I. D. Cole, “On a quasilinear parabolic equation occuring in aerodynamics”, Quart. Appl. Math., 9 (1951), 225–236 | MR | Zbl

[4] B. L. Rozhdestvenskii, N. N. Yanenko, Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1978 | MR

[5] Yu. Ya. Belov, Inverse problems for partial differential equations, VSP, Utrecht etc., 2002 | MR | Zbl

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

[7] V. G. Romanov, Ustoichivost v obratnykh zadachakh, Nauchnyi mir, M., 2005 | MR

[8] N. N. Yanenko, Metod drobnykh shagov resheniya mnogomernykh zadach matematicheskoi fiziki, Nauka, sibirskoe otdelenie, Novosibirsk, 1967 | MR | Zbl

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

[10] A. M. Ilin, A. S. Kalashnikov, O. A. Oleinik, “Lineinye uravneniya vtorogo poryadka parabolicheskogo tipa”, Uspekhi mat. nauk, 17:3 (1962), 3–146 | MR | Zbl

[11] E. Kamke, Spravochnik po differentsialnym uravneniyam v chastnykh proizvodnykh pervogo poryadka, Nauka, M., 1966 | Zbl

[12] V. A. Trenogin, Funktsionalnyi analiz, Nauka, M., 1980 | MR | Zbl

[13] A. N. Tikhonov, A. A. Samarskii, Uravneniya matematicheskoi fiziki, Nauka, M., 1977