The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces

• Main Authors: Luís P. Castro, David Natroshvili
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2006-01-01
• Series: Opuscula Mathematica
• Subjects: Helmholtz equation; boundary-transmission problem; wave diffraction; convolution type operator,; Wiener-Hopf operator; Fredholm property; factorization
• Online Access: http://www.opuscula.agh.edu.pl/vol26/2/art/opuscula_math_2620.pdf

We consider a boundary-transmission problem for the Helmholtz equation, in a Bessel potential space setting, which arises within the context of wave diffraction theory. The boundary under consideration consists of a strip, and certain reactance conditions are assumed on it. Operator theoretical methods are used to deal with the problem and, as a consequence, several convolution type operators are constructed and associated to the problem. At the end, the well-posedness of the problem is shown for a range of regularity orders of the Bessel potential spaces, and for a set of possible reactance numbers (dependent on the wave number).