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

Abstract

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).

Keywords

• Helmholtz equation
• boundary-transmission problem
• wave diffraction
• convolution type operator,
• Wiener-Hopf operator
• Fredholm property
• factorization