Abstract
A study is presented for boundary value problems arising from the wave diffraction theory and involving variable impedance conditions. Two different geometrical situations are considered: the diffraction by a strip and by a half-plane. In the first case, both situations of real and complex wave numbers are analyzed, and in the second case only the complex wave number case is considered. At the end, conditions are founded for the well-posedness of the problems in Bessel potential space settings. These conditions depend on the wave numbers and the impedance properties.
This work was supported in part by Unidade de Investigação Matemática e Aplicações of University of Aveiro, and the Portuguese Science Foundation (FCT-Fundação para a Ciência e a Tecnologia) through the grant number SFRH/BPD/20524/2004.
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Dedicated to W.L. Wendland on the occasion of his 70th birthday
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Castro, L.P., Kapanadze, D. (2008). Diffraction by a Strip and by a Half-plane with Variable Face Impedances. In: Bastos, M.A., Lebre, A.B., Speck, FO., Gohberg, I. (eds) Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications, vol 181. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8684-9_6
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