Opuscula Math. 26, no. 2 (2006), 289-303
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.
Mathematics Subject Classification: 35J05, 35J25, 47A53, 47B35, 47F05, 45E10, 78A45.