Singularities of the scattering kernel for two convex obstacles
type: Item
instance of: scholarly article
title: Singularities of the scattering kernel for two convex obstacles
zbMATH Open document ID: 0699.35202
author: Shin-ichi Nakamura
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1989-01-01T00:00:00Z
review text: The author considers the scattering problem for the wave equation with two finite convex obstacles \({\mathcal O}_ 1\) and \({\mathcal O}_ 2\). The main purpose of the paper is to investigate the location of singularities of the scattering kernel S(s,\(\theta\),\(\omega)\). Set \(r_ i(\omega)=\min \{x\cdot \omega\); \(x\in {\mathcal O}_ i\}\), \(i=1,2\). The first main result says that if \({\mathcal O}_ 1\cap \{x+\ell \omega\); \(x\in {\mathcal O}_ 2\), \(\ell \in {\mathbb{R}}\}=\emptyset\), then S(\(\cdot,-\omega,\omega)\) has only two singularities in the interval [\(\min_{i=1,2}(-2r_ i(\omega)),\infty)\), namely \(-2r_ 1(\omega)\) and \(-2r_ 2(\omega).\) For more restricted \(\omega\) the author describes all singularities of S(s,\(\theta\),\(\omega)\). In case \({\mathcal O}_ i\), \(i=1,2\), are balls similar statements have been obtained by the author and \textit{H. Soga} [J. Math. Soc. Japan 40, No.2, 205-220 (1988; Zbl 0638.35068)].
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 4146674
zbMATH Keywords: two finite convex obstacles
zbMATH Keywords: singularities
zbMATH Keywords: scattering kernel
reviewed by: Plamen Stefanov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195173609
OpenAlex ID: W2146606287
cites work: Q4733016
cites work: Sojourn times and asymptotic properties of the scattering matrix
cites work: Decay of solutions of the wave equation in the exterior of two convex obstacles
cites work: Q3950896
cites work: Q5579836
cites work: Q5645831
cites work: A representation formula for the scattering operator and the inverse problem for arbitrary bodies
cites work: Asymptotic behavior at infinity for Green's functions of first order systems with characteristics of nonuniform multiplicity
cites work: Singularities of the scattering kernel for two balls
cites work: High frequency asymptotics of the scattering amplitude for non-convex bodies
cites work: Q3975552
cites work: Oscillatory integrals with degenerate stationary points and their application to the scattering theory
cites work: Singularities of the scattering kernel for convex obstacles
cites work: Conditions against rapid decrease of oscillatory integrals and their applications to inverse scattering problems
cites work: Grazing rays and reflection of singularities of solutions to wave equations
cites work: Characterization of a convex obstacle by singularities of the scattering kernel
DOI: 10.2977/PRIMS/1195173609
Recommended article: Singularities of the scattering kernel for several convex obstacles
Recommended article: Q3781495
Recommended article: Q3975552
Recommended article: Singularities of the Scattering Kernel and Scattering Invariants for Several Strictly Convex Obstacles
Recommended article: Characterization of a convex obstacle by singularities of the scattering kernel
Recommended article: Q3353477
Recommended article: Q3485329
Recommended article: Singularities of the scattering kernel for trapping obstacles
Recommended article: Singularities of the scattering kernel for two balls
Recommended article: Q3223261
description: scientific article; zbMATH DE number 4146674