Singularities of the scattering kernel for two balls
type: Item
instance of: scholarly article
title: Singularities of the scattering kernel for two balls
zbMATH Open document ID: 0638.35068
author: Shin-ichi Nakamura
author: Hideo Soga
published in: Journal of the Mathematical Society of Japan
publication date: 1988-01-01T00:00:00Z
review text: The authors deal with the scattering by obstacles \({\mathcal O}\) formulated by Lax and Phillips, and consider an inverse problem similar to Majda's. It has been known that the back-scattering S(s,-\(\omega\),\(\omega)\) has at least two singular points for some \(\omega\) if \({\mathcal O}\) is not convex. In this paper, when \({\mathcal O}\) consists of two balls \({\mathcal O}_ 1\) and \({\mathcal O}_ 2\) in \({\mathbb{R}}^ 2\) or \({\mathbb{R}}^ 3\), they examine the whole distribution of the singular points of S(s,-\(\omega\),\(\omega)\) for some \(\omega\), and clarify the relation between this distribution and the distance of \({\mathcal O}_ 1\) and \({\mathcal O}_ 2\).
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 78A05
Mathematics Subject Classification ID: 76Q05
zbMATH DE Number: 4040439
zbMATH Keywords: scattering kernel
zbMATH Keywords: scattering by obstacles
zbMATH Keywords: inverse problem
zbMATH Keywords: back- scattering
zbMATH Keywords: singular points
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04020205
OpenAlex ID: W1969551812
DOI: 10.2969/JMSJ/04020205
description: scientific article; zbMATH DE number 4040439