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

Lafitte, Olivier

Mém. Soc. Math. Fr., Nouv. Sér. 88, viii, 167 p. (2002).

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.

Reviewer: Vladislav Kravchenko (Mexico)

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

Citations:

Zbl 0779.35063