TY  - JOUR
ID  - Castro2006
LB  - Castro2006
AU  - Castro, Luís P.
AU  - Natroshvili, David
TI  - The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces
ST  - The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 2
SP  - 289
EP  - 303
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.2.289
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.2.289
AB  - 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).
KW  - Helmholtz equation
KW  - boundary-transmission problem
KW  - wave diffraction
KW  - convolution type operator
KW  - Wiener-Hopf operator
KW  - Fredholm property
KW  - factorization
SN  - 1232-9274
ER  -