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 "u + k 2 u = 0. We show that the solution u and its far field pattern u ∞ 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.

Multi-parameter analysis of the obstacle scattering problem

Musolino P.
2022

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 "u + k 2 u = 0. We show that the solution u and its far field pattern u ∞ 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.
File in questo prodotto:
File Dimensione Formato  
20220314_PertHelm.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Accesso gratuito (solo visione)
Dimensione 387.4 kB
Formato Adobe PDF
387.4 kB Adobe PDF Visualizza/Apri

I documenti in ARCA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/5005162
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact