Path Argument for Inverse Acoustic and Electromagnetic Obstacle Scattering Problems

Huaian Diao and Hongyu Liu
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Huaian Diao: Jilin University, School of Mathematics
Hongyu Liu: City University of Hong Kong, Department of Mathematics

Chapter Chapter 5 in Spectral Geometry and Inverse Scattering Theory, 2023, pp 113-129 from Springer

Abstract: Abstract Let us recall the acoustic obstacle scattering problem from sound-hard or sound-soft obstacles. To describe the scattering system, we shall use ui, us and u to represent the incident, scattered and total field, respectively, where u = ui + us and u i ( x ) = exp { i k x ⋅ d } $$u^i(x)=\exp \{\mathrm ik\mathbf { x}\cdot \mathbf { d}\}$$ with i = − 1 , d ∈ 𝕊 N − 1 $$\mathrm i=\sqrt {-1},\ \mathbf { d}\in \mathbb S^{N-1}$$ being the incident direction and k > 0 being the wave number. Let D be an impenetrable obstacle, where D is a general compact set in ℝ N ( N ≥ 2 ) $$\mathbb R^N(N\geq 2)$$ with an open connect complement G = ℝ N ∖ D $$G=\mathbb R^N\setminus D$$ .

Date: 2023
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DOI: 10.1007/978-3-031-34615-6_5

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