Identification problem for the wave equation with Neumann data input and Dirichlet data observations

✍ Scribed by Xiaobing Feng; Suzanne Lenhart; Vladimir Protopopescu; Lizabeth Rachele; Brian Sutton

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 441 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00295-x

✦ Synopsis

We seek to identify the dispersive coe cient in a wave equation with Neumann boundary conditions in a bounded space-time domain from imprecise observations of the solution on the boundary of the spatial domain (Dirichlet data). The problem is regularized and solved by casting it into an optimal control setting. By letting the "cost of the control" tend to zero, we obtain the limit of the corresponding control sequence, which we identify with the sought dispersive coe cient. The corresponding solution of the wave equation is interpreted as the possibly nonunique projection of the observation vector onto the range of the Neumann-to-Dirichlet maps corresponding to a single input Neumann data, as the dispersive coe cient is varied. Several numerical examples illustrate the merits and limitations of the procedure.