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Title: Wave diffraction by wedges having arbitrary aperture angle
Author: Castro, L. P.
Kapanadze, D.
Keywords: Wedge diffraction problem
Helmholtz equation
Boundary value problem
Potential operator
Pseudo-differential operator
Cone Sobolev spaces
Weighted Sobolev space
Mellin transform
Fredholm theory
Issue Date: 2015
Publisher: Elsevier
Abstract: The problem of plane wave diffraction by a wedge sector having arbitrary aperture angle has a very long and interesting research background. In fact, we may recognize significant research on this topic for more than one century. Despite this fact, up to now no clear unified approach was implemented to treat such a problem from a rigourous mathematical way and in a consequent appropriate Sobolev space setting. In the present paper, we are considering the corresponding boundary value problems for the Helmholtz equation, with complex wave number, admitting combinations of Dirichlet and Neumann boundary conditions. The main ideas are based on a convenient combination of potential representation formulas associated with (weighted) Mellin pseudo-differential operators in appropriate Sobolev spaces, and a detailed Fredholm analysis. Thus, we prove that the problems have unique solutions (with continuous dependence on the data), which are represented by the single and double layer potentials, where the densities are solutions of derived pseudo-differential equations on the half-line.
Peer review: yes
DOI: 10.1016/j.jmaa.2014.07.080
ISSN: 0022-247X
Appears in Collections:CIDMA - Artigos

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