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Determining the lowest coefficient of a two-dimensional parabolic equation in a domain with a free boundary
Snitko Halyna Anatoliivna 1
1 Department of Mathematical Physics, Institute of applied problems of mechanics and mathematics named after Ya.S. Hairdresser of the National Academy of Sciences, Lviv, 79060, Ukraine
Keywords: a two-dimensional parabolic equation, the inverse problem, time-dependent functions
Abstract
The unique solvability conditions of the inverse problem of nding the minor coefficient in a two-dimensional parabolic equation in the domain for which the location of boundary part is described by the unknown time-dependent functions are established.
References

[1]  Cannon J.R., Lin Y., Wang S. Determination of a control parameter in a parabolic partial differential equation // J. Austral. Math. Soc. Ser. B. - 1991. - 33 , № 2. - P. 149-163.

[2] Mamayusupov O.Sh. About determination of parabolic equation coefficient // Studies on integro-differential equations (Frunze). -1989. - Vyp. 22. - P. 157-160.

[3] Ivanchov N.I. On the inverse problem of simultaneous determination of heat conductivity and heat capacity coefficients // Sib. mat. zhurn. - 1994. - 35, № 3. - P. 612-621.

[4]  Koval'chuk S.M. Determination of the coefficient of thermal conductivity and heat capacity per unit volume in a multilayer medium // J. Math. Sci. - 1998. - 90 , № 2. - P. 2042-2047.

[5] Pabirivskaia N.V. Inverse problems with integral redefinition conditions // Mat. methody i fiziko-mekh. polya. 2000. - 43 , № 1. - С. 51-58.

[6] Savateev E.G. Reduction of the inverse problem for the parabolic type equation // Dokl. RAS. - 1994. - 334, № 5. - P. 562-563.

[7] Ivanchev M.I. Inverse problem with a free boundary for the heat conduction equation // Ukrainian Mathematical Journal - 2003. - 55 , № 7. - P. 901-910.

[8] Baranska I. Determination of the senior coefficient in a parabolic equation in a region with unknown boundaries // Lviv Univ. Ser. meh.-mat. - 2005. - Issue 64. - P. 20-38.

[9]  Баранська I.Є. Обернена задача в областi з вiльною межею для двовимiрного параболiчного  рiвняння // Мат. методи та фiз.-мех. поля. - 2007. - 50 , № 2.- С. 17-28.

[10]  Баранська I.Є., Iванчов М.I. Обернена задача для двовимiрного рiвняння теплопровiдностi в областi з вiльними межами // Укр. мат. вiсник. -  2007. - 4 , № 4. - С. 457-484.

[11] Ladyzhenskaya O.A., Solonnikov V.A., Uraltseva N.N. Linear and quasilinear equations of parabolic type. - Moscow: Nauka, 1967. - 736 p.

[12]  Ivanchov M. Inverse problems for equations of parabolic type // Lviv: VNTL Publ., 2003. - 238 p. - (Math. Studies: Monograph Ser. - Vol. 10.)

Cite
ACS Style
Snitko , H.A. Determining the lowest coefficient of a two-dimensional parabolic equation in a domain with a free boundary. Bukovinian Mathematical Journal. 2016, 3
AMA Style
Snitko HA. Determining the lowest coefficient of a two-dimensional parabolic equation in a domain with a free boundary. Bukovinian Mathematical Journal. 2016; 3(2).
Chicago/Turabian Style
Halyna Anatoliivna Snitko . 2016. "Determining the lowest coefficient of a two-dimensional parabolic equation in a domain with a free boundary". Bukovinian Mathematical Journal. 3 no. 2.
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