Diffraction by a right-angled no-contrast penetrable wedge: recovery of far-field asymptotics

2023/10/30 by Kunz, Valentin D., Assier, Raphael C.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.19892

Abstract

We provide a description of the far-field encountered in the diffraction problem resulting from the interaction of a monochromatic plane-wave and a right-angled no-contrast penetrable wedge. To achieve this, we employ a two-complex-variable framework and use the analytical continuation formulae derived in (Kunz & Assier, QJMAM, 76(2), 2023) to recover the wave-field's geometrical optics components, as well as the cylindrical and lateral diffracted waves. We prove that the corresponding cylindrical and lateral diffraction coefficients can be expressed in terms of certain two-complex-variable spectral functions, evaluated at some given points.

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