Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 858516, 10 pages
http://dx.doi.org/10.1155/2014/858516
Research Article

On an Inverse Boundary Value Problem for a Fourth Order Elliptic Equation with Integral Condition

Baku State University, 1148 Baku, Azerbaijan

Received 22 December 2013; Accepted 16 February 2014; Published 24 March 2014

Academic Editor: Jaan Janno

Copyright © 2014 Yashar T. Mehraliyev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. I. Tikhonov, “On the stability of inverse problems,” Doklady Akademii Nauk SSSR, vol. 39, no. 5, pp. 195–198, 1943. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. M. Lavrent'ev, “On an inverse problem for the wave equation,” Doklady Akademii Nauk SSSR, vol. 157, no. 3, pp. 520–521, 1964. View at Google Scholar · View at MathSciNet
  3. M. M. Lavrent'ev, V. G. Romanov, and S. P. Shishatsky, Ill-posed Problems of Mathematical Physics and Analysis, Nauka, Moscow, Russia, 1980. View at MathSciNet
  4. A. M. Denisov, Introduction to Theory of Inverse Problems, MSU, East Lansing, Mich, USA, 1994.
  5. M. I. Ivanchov, Inverse Problems for Equations of Parabolic Type, VNTL Publishers, Lviv, Ukraine, 2003. View at MathSciNet
  6. M. I. Īvanchov and N. V. Pabirivs'ka, “Simultaneous determination of two coefficients in a parabolic equation in the case of nonlocal and integral conditions,” Ukrainian Mathematical Journal, vol. 53, no. 5, pp. 589–596, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. I. Īvanchov, “An inverse problem with a free boundary for the heat equation,” Ukrainian Mathematical Journal, vol. 55, no. 7, pp. 901–910, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  8. A. I. Prilepko and A. B. Kostin, “Some inverse problems for parabolic equations with final and integral observation,” Matematichesky Sbornik, vol. 183, no. 4, pp. 49–68, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  9. A. I. Prilepko and D. S. Tkachenko, “Properties of solutions of a parabolic equation and the uniqueness of the solution of the inverse source problem with integral overdetermination,” Zhurnal Vychislitelnoi Matematiki and Matematicheskoy Fiziki, vol. 43, no. 4, pp. 562–570, 2003 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. V. L. Kamynin, “On an inverse problem of determining the right-hand side of a parabolic equation with the integral overdetermination condition,” Matematicheskie Zametki, vol. 77, no. 4, pp. 522–534, 2005 (Russian). View at Publisher · View at Google Scholar · View at MathSciNet
  11. V. V. Solov'ev, “Inverse problems of source determination for the Poisson equation on the plane,” Zhurnal Vychislitelnoi Matematiki and Matematicheskoy fiziki, vol. 44, no. 5, pp. 862–871, 2004 (Russian). View at Google Scholar · View at MathSciNet
  12. V. V. Solov'ev, “Inverse problems for elliptic equations on the plane. I,” Differentsial'nye Uravneniya, vol. 42, no. 8, pp. 1106–1114, 2006 (Russian). View at Publisher · View at Google Scholar · View at MathSciNet
  13. M. M. Hajiyev, “An inverse problem for a degenerate elliptic equation,” in Application of Functional Analysis Methods in Mathematical Physics Equations, pp. 66–71, Nauk SSSR, Novosibirsk, Russia, 1987. View at Google Scholar · View at MathSciNet
  14. Y. T. Mehraliyev, “Inverse boundary value problem for a second order elliptic equation with additional integral condition,” Vestnik Udmurtskogo Universiteta Matematika, no. 1, pp. 32–40, 2012 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Y. T. Mehraliyev, “On solvability of an inverse boundary value problem for a second order elliptic equation,” Vestnic Tverskogo Gosudarstvennogo, no. 23, pp. 25–38, 2011 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Y. T. Mehraliyev, “An inverse boundary value problem for a fourth order elliptic equation,” Proceedings of Institute of Mathematics and Mechanics. National Academy of Sciences of Azerbaijan, vol. 36, pp. 75–90, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. K. I. Khudaverdiyev and A. A. Veliyev, Investigation of One-Dimensional Mixed Problem for a Class of Pseudohyperbolic equations of Third Order with Nonlinear Operator Right Side, Chashyoglu, Baku, Azerbaijan, 2010.