Far Eastern Mathematical Journal

To content of the issue


On the problem of the identification of some multy-dimensional parabolic equation coefficients in the case of non-homogeneous overdetermination conditions


S. N. Baranov, Yu. Ya. Belov

2004, issue 1, Ñ. 30–40


Abstract
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.

Keywords:
differential equation, parabolic equation, inverse problems, redefinition condition, method of weak approximation

Download the article (PDF-file)

References

[1] S. S. Akhtamova, Yu. Ya. Belov, “On some inverse problems for parabolic equations”, Soviet. Math. Dokl., 43:1 (1991), 166–170
[2] Yu. E. Anikonov, Yu. Ya. Belov, “Determining two unknown coefficients of parabolic type equations”, J. Unv. Ill. Posed Problems, 8 (2000), 1–19
[3] Yu. Ya. Belov, S. V. Polynceva, “Ob odnoj obratnoj zadache s dvumya neizvestnymi koe'fficientami”, Tr. III mezhdunar. konf. “Simmetriya i differencial'nye 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
[5] S. N. Baranov, Yu. Ya. Belov, “O zadache identifikacii dvux koe'fficientov s neodnorodnymi usloviyami pereopredeleniya”, Neklassicheskie uravneniya matematicheskoj fiziki, Sb. nauch. rabot, red. 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
[7] S. N. Baranov, Yu. Ya. Belov, “O zadache identifikacii trex koe'fficientov s neodnorodnymi usloviyami pereopredeleniya”, Vychislitel'nye texnologii, 8:4 (2003), 92–102
[8] N. N. Yanenko, Metod drobnyx shagov resheniya mnogomernyx zadach matematicheskoj fiziki, Novosibirsk, 1967
[9] Yu. Ya. Belov, S. A. Kantor, Metod slaboj approksimacii, Krasnoyar. gos. un-t, Krasnoyarsk, 1999
[10] L. S. Pontryagin, Obyknovennye differencial'nye uravneniya, Nauka, M., 1965
[11] A. M. Il'in, A. S. Kalashnikov, O. A. Olejnik, “Linejnye uravneniya vtorogo poryadka parabolicheskogo tipa”, Uspexi mat. Nauk, 17:3 (1962), 3–146.

To content of the issue