The impedance problem of wave diffraction by a trip with higher order boundary conditions

Abstract

This work is devoted to analyse 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. A constructive approach of operator relations is built, which allows a transparent interpretation of the problem in an operator theory framework. 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. In particular, a Fredholm characterization of the problem is obtained in terms of the initial space order parameters.At the request of the author and the Proceedings Editor the above article has been replaced with a corrected version. original PDF file supplied to AIP Publishing contained an error in the title of the article. original title appeared as: The Impedance Problem of Wave Diffraction by a trip with Higher Order Boundary Conditions. This article has been replaced and the title now appears correctly online. corrected article was published on 8 November 2013.This work is devoted to analyse 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. A constructive approach of operator relations is built, which allows a transparent interpretation of the problem in an operator theory framework. 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. In particular, a Fredholm characterization of the problem is obtained in terms of the initial space order parameters.At the request of the author and the Proceedings Editor the above article has been replaced with a corrected version. original PDF file supplied to AIP Publishing contained an error in the title of the article. original title appeared as: The Imp...