Multi-parameter analysis of the obstacle scattering problem. (1st May 2022)

• Record Type: Journal Article
• Authors: Dalla Riva, Matteo; Luzzini, Paolo; Musolino, Paolo
• Is Part Of: Inverse problems. Volume 38:Number 5(2022)
• Publication Date: 2022-05-01
• Subjects: Helmholtz equation -- acoustic scattering -- associated exterior Dirichlet problem -- Dirichlet-to-Neumann operator -- shape sensitivity analysis -- perturbed domain -- integral equations; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac5eea
• Languages: English
• ISSNs: 0266-5611

Abstract

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 Δ 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.