Mixed boundary value problems of diffraction by a half-plane with an obstacle perpendicular to the boundary

作者：Castro Luis P^*; Kapanadze David

来源：Mathematical Methods in the Applied Sciences, 2014, 37(10): 1412-1427.

DOI：10.1002/mma.2900

• Helmholtz equation
• wave diffraction
• boundary value problems
• potential method
• oscillating symbols

The paper is devoted to the analysis of wave diffraction problems modeled by classes of mixed boundary conditions and the Helmholtz equation, within a half-plane with a crack. Potential theory together with Fredholm theory, and explicit operator relations, are conveniently implemented to perform the analysis of the problems. In particular, an interplay between Wiener-Hopf plus/minus Hankel operators and Wiener-Hopf operators assumes a relevant preponderance in the final results. As main conclusions, this study reveals conditions for the well-posedness of the corresponding boundary value problems in certain Sobolev spaces and equivalent reduction to systems of Wiener-Hopf equations.

• 出版日期2014-7-15