On the use of \(T\)-coercivity to study the interior transmission eigenvalue problem
type: Item
instance of: scholarly article
title: On the use of \(T\)-coercivity to study the interior transmission eigenvalue problem
zbMATH Open document ID: 1244.35099
author: A.-S. Bonnet-Ben Dhia
author: Lucas Chesnel
author: Houssem Haddar
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2011-07-08T00:00:00Z
review text: The paper is devoted to the study of the so-called interior transmission problem (in the scalar case when the contrast in the scattering medium occurs in two independent functions) by developing the \(T\)-coercivity approach; cf. [\textit{A. S. Bonnet-Ben Dhia}, \textit{P. Ciarlet jun.} and \textit{C. M. Zwölf}, J. Comput. Appl. Math. 234, No. 6, 1912--1919 (2010; Zbl 1202.78026); erratum \textit{A. S. Bonnet-Ben Dhia} and \textit{P. Ciarlet jun.}, ibid. 234, No. 8, 2616 (2010; Zbl 1266.78026)]. The authors obtain conditions to ensure the Fredholm property of the operator associated with the problem and prove that the set of interior transmission eigenvalues is discrete. Change sign situations of the difference between the inclusion index and the background index are included in this study, and consequent Faber-Krahn type inequalities are obtained.
reviewed by: L. P. Castro
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 5919175
zbMATH Keywords: interior transmission problem
zbMATH Keywords: coercivity
zbMATH Keywords: wave diffraction problem
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: Fredholm property
MaRDI profile type: Publication
full work available at URL: j.crma.2011.05.008
OpenAlex ID: W1985697506
cites work: Time harmonic wave diffraction problems in materials with sign-shifting coefficients
cites work: The linear sampling method for anisotropic media
cites work: The Existence of an Infinite Discrete Set of Transmission Eigenvalues
cites work: On the interior transmission eigenvalue problem
cites work: The interior transmission problem
cites work: The Interior Transmission Problem and Inverse Scattering from Inhomogeneous Media
DOI: 10.1016/J.CRMA.2011.05.008
description: scientific article; zbMATH DE number 5919175