Abstract
We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Delta u + k (2) u = 0. We show that the solution u and its far field pattern u (infinity) depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.
Original language | English |
---|---|
Pages (from-to) | 055004 |
Journal | Inverse Problems |
Volume | 38 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- Dirichlet-to-Neumann operator
- Helmholtz equation
- acoustic scattering
- associated exterior Dirichlet problem
- integral equations
- perturbed domain
- shape sensitivity analysis