Variational approach for identifying a coefficient of the wave equation

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Abstract

An inverse initial-boundary value problem for identifying the coefficient of some second order hyperbolic equation by single set of boundary measurement is considered. The problem is transformed to a minimization problem of a functional. After a concrete expression of the Gateaux derivative of the functional is obtained, an algorithm for identifying the coefficient is given based on the projected gradient method. A numerical result is presented to verify the algorithm.

Keywords

lnverse initial-boundary value problem , coefficient identification , wave equation , variational method , projected gradient method
  • Cheok Choi Department of Mathematics, Seoul National University 56-1 Shillim-dong, kwanak-ku, Seoul 151-742, Korea.
  • Gen Nakamura Graduate School of Science, Hokkaido University, Kita 8, Nishi 5, Kita-ku, Sapporo, Hokkaido 060-0808, Japan.
  • Kenji Shirota Faculty of Science, lbaraki University, Bunkyo 2-1-1, Mito, Ibaraki 310-8512, Japan.
  • Pages: 81-101
  • Date Published: 2007-08-01
  • Vol. 9 No. 2 (2007): CUBO, A Mathematical Journal

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Published

2007-08-01

How to Cite

[1]
C. Choi, G. Nakamura, and K. Shirota, “Variational approach for identifying a coefficient of the wave equation”, CUBO, vol. 9, no. 2, pp. 81–101, Aug. 2007.

Issue

Vol. 9 No. 2 (2007): CUBO, A Mathematical Journal

Section

Articles