Pointwise and internal controllability for the wave equation
type: Item
instance of: scholarly article
title: Pointwise and internal controllability for the wave equation
zbMATH Open document ID: 1077.93003
published in: Applied Mathematics and Optimization
publication date: 2003-08-18T00:00:00Z
review text: The authors consider the observation and control of the one-dimensional wave equation on \(\varphi = [0,\ell]\times [0,T]\) with observation and control restricted to a small spatial subinterval \([0,0+\varepsilon]\subset (0,\ell)\). The main interest is in the asymptotics as \(\varepsilon\to 0,\) i.e., as the subinterval shrinks to the single point \(\{a\}\). In previous papers, quoted by the authors, results were obtained showing an essential dependence on number-theoretic properties of \(a/\ell\) -- with a distinction between ``good'' points for which the asymptotics behave well and ``bad'' points for which they do not. The principal novelty of the paper is the introduction of a natural contextual change which makes the asymptotics behave well for all choices of the point \(a\in (0,\ell)\).
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L40
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1966419
author: Sergei Avdonin
author: Thomas I. Seidman
reviewed by: Gheorghe Aniculăesei
MaRDI profile type: Publication
full work available at URL: s00245-002-0747-1
OpenAlex ID: W1991018163
DOI: 10.1007/S00245-002-0747-1
description: scientific article; zbMATH DE number 1966419