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The wave diffracted by a wedge with mixed boundary conditions. (English) Zbl 1017.35007

The diffraction problem on a curved wedge in \(\mathbb{R}^2\), each face \(+\) or \(-\) of the wedge being characterized by a mixed boundary condition of impedance type \(\partial_{n}u+z^{\pm}(x)\partial_{t}u=0\) is studied. The work is a generalization of the results of P. Gérard and G. Lebeau [J. Am. Math. Soc. 6, 341-424 (1993; Zbl 0779.35063)] where the Dirichlet boundary condition was considered. The problem is reduced to a system of the two traces of the diffracted wave on each face of the wedge, the diffraction coefficients are calculated.

MSC:

35A21 Singularity in context of PDEs
35L05 Wave equation
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35Q60 PDEs in connection with optics and electromagnetic theory
78A45 Diffraction, scattering

Citations:

Zbl 0779.35063
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