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Azerbaijan Baku
Section Mathematics
Title Inverse boundary value problem for second order elliptic equation with additional integral condition
Author(-s) Megraliev Ya.T.a
Affiliations Baku State Universitya
Abstract An inverse boundary value problem for the second order elliptic equation with an additional integral condition of the first kind is investigated. We introduce the definition of a classical solution for the considered inverse boundary value problem reduced to solving of the system of integral equations by the use of the Fourier method. First, the existence and uniqueness of solutions of the system of integral equations are proved by using the method of contraction mappings; and then the existence and uniqueness of classical solutions of the original problem are proved.
Keywords inverse boundary value problem, elliptic equation, Fourier method, classic solution
UDC 517.95
MSC 35-02
DOI 10.20537/vm120104
Received 19 December 2011
Language Russian
Citation Megraliev Ya.T. Inverse boundary value problem for second order elliptic equation with additional integral condition, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 1, pp. 32-40.
  1. Samarskii A.A. On some problems of the theory of differential equations, Differ. Uravn., 1980, vol. 16, no. 11, pp. 1925–1935.
  2. Cannon J.R. The solution of the heat equation subject to the specification of energy, Quart. Appl. Math., 1963, vol. 5, no. 21, pp. 155–160.
  3. Ionkin N.I. Solutions of boundary value problem in heat conductions theory with nonlocal boundary conditions, Differ. Uravn., 1977, vol. 13, no. 2, pp. 294–304.
  4. Nakhushev A.M. A method of approximation of solving the boundary value problems for the differential equations and its approximation to dynamics of soil moisture and ground water, Differ. Uravn., 1982, vol. 18, no. 1, pp. 72–81.
  5. Kapustin N.Yu., Moiseev E.I. On the spectral problems with the spectral parameter under the boundary condition, Differ. Uravn., 1997, vol. 33, no. 1, pp. 115–119.
  6. Kozhanov A.I., Pul’kina L.S. On the solvability of boundary-value problems with the non-local boundary condition of integral form for the multidimensional hyperbolic equations, Differ. Uravn., 2006, vol. 42, no. 9, pp. 1166–1179.
  7. Gordeziani D.G., Avalishvili G.A. On the constructing of solutions of the non-local initial boundary value problems for one-dimensional medium oscillation equations, Mat. Model., 2000, vol. 12, no. 1, pp. 94–103.
  8. Prilepko A.I., Kostin A.B. On some inverse problems for the parabolic equations with the final and integral observation, Mat. Sb., 1992, vol. 183, no. 4, pp. 49–68.
  9. Prilepko A.I., Tkachenko D.S. Properties of the solutions of parabolic equation and the uniqueness of solution of the reverse problem about the source with the integral redefining, Zh. Vychisl. Mat. Mat. Fiz., 2003, vol. 43, no. 4, pp. 562–570.
  10. Kamynin V.L. On the inverse problem of determining the right side in the parabolic equation with the condition of integral redefining, Mat. Zametki, 2005, vol. 77, no. 4, pp. 522–534.
  11. Naimark M.A. Lineinye differentsial’nye operatory (Linear differential operators), Moscow: Nauka, 1969, 526 p.
  12. Khudaverdiev K.I., Veliev A.A. Issledovanie odnomernoi zadachi dlya odnogo klassa psevdogiperbolicheskikh uravnenii tret’ego poryadka s nelineinoi pravoi chast’yu (Investigation of the one-dimensional mixed problem for a class of the pseudo-hyperbolic equations of the third order with the nonlinear operator at the right-hand side), Baku: Chashyogly, 2010, 168 p.
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