Open AccessA Wave Diffraction Problem with Higher Order Impedance Boundary Conditions
Author(s) -
A. M. Simões
Publication year - 2022
Publication title -
international journal of mathematical models and methods in applied sciences
Language(s) - English
Resource type - Journals
ISSN - 1998-0140
DOI - 10.46300/9101.2022.16.12
Subject(s) - mathematics , sobolev space , mathematical analysis , boundary value problem , operator (biology) , helmholtz equation , diffraction , physics , biochemistry , chemistry , repressor , transcription factor , optics , gene
In this paper, we consider an impedance boundary transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. Operator theoretical methods and relations between operators are built to deal with the problem and, as consequence, a transparent interpretation of the problem in an operator theory framework are associated to the problem. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. At the end, we describe when the operators associated with the problem enjoy the Fredholm property in terms of the initial space order parameters.