268
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Determination of the leading coefficient in fourth-order Sturm–Liouville operator from boundary measurements

&
Pages 413-424 | Received 09 Oct 2006, Accepted 16 Jan 2007, Published online: 12 Jun 2008

References

  • Papanicolau, V, 1995. The spectral theory of the vibrating periodic beam, Communications in Mathematical Physics 170 (1995), pp. 359–373.
  • Papanicolau, VG, and Kravvaritis, D, 1997. An inverse spectral problem for the Euler–Bernoulli equation for the vibrating beam, Inverse Problems 13 (1997), pp. 1083–1092.
  • Gelfand, IM, and Levitan, BM, 1951. On the determination of a differential equation from its spectral function, Transactions of the American Mathematical Society, Series 2 1 (1951), pp. 253–304.
  • Hochstedt, H, 1973. The inverse Sturm–Liouville problem, Communications of Pure and Applied Mathematics 26 (1973), pp. 715–729.
  • Barcilon, V, 1982. Inverse problem for a vibration beam in a free-clamped configuration, Philosophical Transactions of Royal Society 304 (1982), pp. 211–251.
  • McLaughlin, JR, 1984. "On constructing solutions to an inverse Euler–Bernoulli problem". In: Santosa, F, ed. Inverse Problems of Acoustic and Elastic Waves. Philadelphia: SIAM; 1984. pp. 341–347.
  • Barcilon, V, 1987. Sufficient conditions for the solution of the inverse problem for a vibrating beam, Inverse Problems 3 (1987), pp. 181–193.
  • Lowe, B, and Rundell, W, 1994. An inverse problem for a Sturm–Liouville operator, Journal of Mathematical Analysis and Applications 181 (1994), pp. 188–199.
  • Lesnic, D, Elliott, L, and Ingham, DB, 1999. Analysis of coefficient identification problems associated to the Euler–Bernoulli beam theory,, The IMA Journal of Applied Mathematics 62 (1999), pp. 101–116.
  • White, LW, 1989. Identification of flexural rigidity in a dynamic plate model, Journal of Mathematical Analysis and Applications 144 (1989), pp. 275–303.
  • Lesnic, D, 2005. "An inverse coefficient identification problem in a dynamic plate model". In: Lesnic, D, ed. The 5th International Conference on Inverse Problems in Engineering: Theory and Practice. Leeds: Leeds University Press; 2005. pp. L05.1–L05.10.
  • Hasanov, A, and Shores, TS, 1997. Solution of an inverse coefficient problem for an ordinary differential equation, Applicable Analysis 67 (1997), pp. 11–20.
  • Seyidmamedov, Z, and Hasanov, A, 2002. Determination of leading coefficients in Sturm–Liouville operator from boundary measurements, I. A stripping algorithm, Applied Mathematics and Computation 125 (2002), pp. 1–21.
  • Hasanov, A, and Seyidmamedov, Z, 2002. Determination of leading coefficients in Sturm–Liouville operator from boundary measurements, II. Unicity and an engineering approach, Applied Mathematics and Computations 125 (2002), pp. 23–34.
  • Hasanov, A, 2003. An inverse polynomial method for the identification of the leading coefficient in the Sturm–Liouville operator from boundary measurements, Applied Mathematics and Computation 140 (2003), pp. 501–515.
  • Hasanov, A, 2004. Error analysis of a multi-singular inverse coefficient problem for the Sturm–Liouville operator from boundary measurements, Applied Mathematics and Computation 150 (2004), pp. 493–524.
  • Hasanov, A, 2004. The determination of the leading coefficient in the monotone potential Sturm–Liouville operator from boundary measurements, Applied Mathematics and Computation 152 (2004), pp. 141–162.
  • Lesnic, D, 2006. Determination of the flexural rigidity of a beam from limited boundary measurements, Journal of Applied Mathematics and Computing 20 (2006), pp. 17–34.
  • Samarskii, AA, 2001. The theory of finite difference schemes. New York: Marcel Decker; 2001.
  • Morozov, V, 1966. On the solution of functional equations by the method of regularization, Soviet Mathematics Doklady 7 (1966), pp. 414–417.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.