On continuous dependence for an inverse initial boundary value problem for the wave equation
type: Item
instance of: scholarly article
title: On continuous dependence for an inverse initial boundary value problem for the wave equation
zbMATH Open document ID: 0733.35107
DOI: 10.1016/0022-247X(90)90207-V
author: Ziqi Sun
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The author studies the continuous dependence of the coefficient q in an initial boundary value problem for the wave equation \(u_{tt}=\Delta u+qu\) on the Neumann to Dirichlet map for this problem. This is shown by first proving an orthogonality result for any two pairs \((q_ 1,u_ 1)\), \((q_ 2,u_ 2)\) of solutions. Then a result of Rakesh and Symes (1988) is used to construct a family of special solutions \(u_ 1\) and \(u_ 2\). Using these special solutions gives an estimate for the Fourier transform of \(q_ 1-q_ 2\). Under the assumption that \(q_ 1-q_ 2\in H^{\alpha}({\mathbb{R}}^ n)\) for some \(\alpha >0\) he finally derives the desired estimates.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 4212656
zbMATH Keywords: parameter identification
zbMATH Keywords: continuous dependence
zbMATH Keywords: Neumann to Dirichlet map
reviewed by: Andreas Kirsch
MaRDI profile type: Publication
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full work available at URL: 0022-247x(90)90207-v
OpenAlex ID: W1998774301
description: scientific article; zbMATH DE number 4212656