Affiliation:
1. Center of Mathematics - University of Beira Interior (CM-UBI), Department of Mathematics of University of Beira Interior, 6200-001 Covilha, Portugal
Abstract
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.
Publisher
North Atlantic University Union (NAUN)
Subject
Applied Mathematics,Computational Mathematics,Mathematical Physics,Modeling and Simulation