On the problem of the identification of some multy-dimensional parabolic equation coefficients in the case of non-homogeneous overdetermination conditions
Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 30-40.

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In this article we consider a problem of determining three unknown highest coefficients of many-dimensional parabolic equation for Cauchy data. We prove the theorems of existence and uniqueness of solution in the small for the classical inverse problem. To prove the existence solvability of problem, we will use the method of week approximation.
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S. N. Baranov; Yu. Ya. Belov. On the problem of the identification of some multy-dimensional parabolic equation coefficients in the case of non-homogeneous overdetermination conditions. Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 1, pp. 30-40. http://geodesic.mathdoc.fr/item/DVMG_2004_5_1_a4/

[1] S. S. Akhtamova, Yu. Ya. Belov, “On some inverse problems for parabolic equations”, Soviet. Math. Dokl., 43:1 (1991), 166–170 | MR | Zbl

[2] Yu. E. Anikonov, Yu. Ya. Belov, “Determining two unknown coefficients of parabolic type equations”, J. Unv. Ill. Posed Problems, 8 (2000), 1–19 | MR

[3] Yu. Ya. Belov, S. V. Polyntseva, “Ob odnoi obratnoi zadache s dvumya neizvestnymi koeffitsientami”, Tr. III mezhdunar. konf. “Simmetriya i differentsialnye uravneniya”, IVM SO RAN, Krasnoyarsk, 2002, 60–65

[4] A. Lorenzi, E. Paparoni, “Identification of two unknown coefficients in integro-differential operator equations”, J. Unv. Ill. Posed Problems, 1:4 (1993), 331–348 | DOI | MR | Zbl

[5] S. N. Baranov, Yu. Ya. Belov, “O zadache identifikatsii dvukh koeffitsientov s neodnorodnymi usloviyami pereopredeleniya”, Neklassicheskie uravneniya matematicheskoi fiziki, Sb. nauch. rabot, ed. A. I. Kozhanov, In-t matematiki, Novosibirsk, 2002

[6] Yu. Ya. Belov, Inverse Problem for Partial Differential Equations, VSP. Utrecht, The Netherlands, 2002, 211 pp. | MR | Zbl

[7] S. N. Baranov, Yu. Ya. Belov, “O zadache identifikatsii trekh koeffitsientov s neodnorodnymi usloviyami pereopredeleniya”, Vychislitelnye tekhnologii, 8:4 (2003), 92–102

[8] N. N. Yanenko, Metod drobnykh shagov resheniya mnogomernykh zadach matematicheskoi fiziki, Novosibirsk, 1967

[9] Yu. Ya. Belov, S. A. Kantor, Metod slaboi approksimatsii, Krasnoyar. gos. un-t, Krasnoyarsk, 1999

[10] L. S. Pontryagin, Obyknovennye differentsialnye uravneniya, Nauka, M., 1965 | MR | Zbl

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