## 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

### Keywords:

diffraction coefficients; impedance

Zbl 0779.35063
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