Variational approach for identifying a coefficient of the wave equation

Cheok Choi; Gen Nakamura; Kenji Shirota

Authors

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.

Keywords:

lnverse initial-boundary value problem, coefficient identification, wave equation, variational method, projected gradient method

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.