Uniqueness for an inverse problem for the wave equation in the half space
type: Item
instance of: scholarly article
title: Uniqueness for an inverse problem for the wave equation in the half space
zbMATH Open document ID: 0867.35114
author: Shin-ichi Nakamura
published in: Tokyo Journal of Mathematics
publication date: 1996-09-15T00:00:00Z
review text: Consider the initial and boundary value problem \[ u_{tt}-\Delta_xu+ b(x)u_t+a(x)u=0,\quad\text{in }\mathbb{R}^n_+\times(0,T), \] \[ u=u_t=0\quad\text{on }\mathbb{R}^n_+\times\{0\},\;\partial_zu(y,0,t)=f(y,t)\quad\text{on }\mathbb{R}^{n-1}\times(0,T). \] Here, \(a\) is bounded, \(b\) is \(C^2\) smooth and both \(a\) and \(b\) are assumed to be constant for \(|x|>r\). The author proves that for \(T>(\pi+1)r\), the Neumann-to-Dirichlet map uniquely determines the coefficients \(a\) and \(b\).
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 927042
zbMATH Keywords: uniqueness
zbMATH Keywords: wave equation
zbMATH Keywords: half space
zbMATH Keywords: Dirichlet-to-Neumann map
reviewed by: Dang Dinh Ang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270043228
OpenAlex ID: W1975165351
DOI: 10.3836/TJM/1270043228
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description: scientific article; zbMATH DE number 927042