Determining the potential in a wave equation without a geometric condition. Extension to the heat equation
type: Item
instance of: scholarly article
title: Determining the potential in a wave equation without a geometric condition. Extension to the heat equation
zbMATH Open document ID: 1346.35226
author: Kaïs Ammari
author: Mourad Choulli
author: Faouzi Triki
published in: Proceedings of the American Mathematical Society
publication date: 2016-08-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1509.09078
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 6620003
zbMATH Keywords: inverse problem
zbMATH Keywords: wave equation
zbMATH Keywords: potential
zbMATH Keywords: boundary measurements
MaRDI profile type: Publication
OpenAlex ID: W2962982524
arXiv ID: 1509.09078
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DOI: 10.1090/PROC/13069
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review text: The paper deals with the initial-boundary value problem for the wave equation NEWLINE\[NEWLINE\begin{cases} \partial_t^2u-\Delta u+q(x)u=0,\text{ in }Q=\Omega\times (0,\tau),\\ u=0,\text{ on }\Sigma=\Gamma\times (0,\tau),\\ u(\cdot,0)=u_0,\quad \partial_tu(\cdot,0)=0, \end{cases}\tag{P}NEWLINE\]NEWLINE where \(\Omega\) is a \(C^3\)-smooth bounded domain of \(\mathbb{R}^n\), \(n\geq 2\), with boundary \(\Gamma\). Using a spectral decomposition method and an interpolation inequality established by L. Robbiano, the authors prove a logarithmic stability estimate for the inverse problem of determining the potential \(q\) in (P) from boundary measurements. An inverse coefficient problem for the heat equation is also investigated.
reviewed by: Rodica Luca
description: scientific article; zbMATH DE number 6620003