Multi-parameter analysis of the obstacle scattering problem

Matteo Dalla Riva, PAOLO LUZZINI, Paolo Musolino

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)055004
JournalInverse Problems
Volume38
Issue number5
DOIs
Publication statusPublished - 2022

Keywords

  • Dirichlet-to-Neumann operator
  • Helmholtz equation
  • acoustic scattering
  • associated exterior Dirichlet problem
  • integral equations
  • perturbed domain
  • shape sensitivity analysis

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