WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
Fredholm Characterization for a Wave Diffraction Problem with Higher Order Boundary Conditions: Impedance Case
Author:
Abstract: In this paper, a Fredholm characterization for operators related to a wave diffraction problem with higher order impedance boundary conditions is developed. We consider an impedance boundary transmission problem for the Helmholtz equation. The problem will be analysed in an operator theory viewpoint and is considered within a framework of Bessel potential spaces. Relations between operators and extension methods 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. Different types of operator relations are exhibited for different types of operators acting between Lebesgue and Bessel potential spaces on a finite interval and on the positive half-line. At the end, we describe when the operators associated with the problem enjoy the Fredholm property with Fredholm index equal to zero in terms of the initial space order parameters. In addition, an operator normalization method is applied.
Search Articles
Keywords: Higher order impedance boundary condition, wave diffraction, Helmholtz equation, Bessel potential space, convolution type operator, Wiener-Hopf operator, Fredholm property, normalization
Pages: 535-546
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #52