Controllability of an elliptic equation and its finite difference approximation by the shape of the domain
type: Item
instance of: scholarly article
title: Controllability of an elliptic equation and its finite difference approximation by the shape of the domain
zbMATH Open document ID: 1045.93023
author: Enrique Zuazua
author: D. Chenais
published in: Numerische Mathematik
publication date: 2003-08-19T00:00:00Z
review text: The authors consider the controllability problem (rarely investigated in the literature) for an elliptic PDE with respect to the shape of the domain where the equation holds. The authors prove the approximate controllability for the linearized system and give a detailed discussion for the controllability of the discrete problem. They point out main difficulties that e.g. do not allow to say anything about convergence of shapes when the discretization step tends to zero. An interesting introduction to problems of controllability for PDE's can be found in \textit{J. L. Lions}'s books [Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1: Contrôlabilité exacte (1988; Zbl 0653.93002); Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 2: Perturbations (1988; Zbl 0653.93003)] and in the papers by \textit{E. Zuazua} [``Some problems and results on the controllability of partial differential equations'', Prog. Math. 169, 276--311 (1998; Zbl 1126.35305); Discrete Contin. Dyn. Syst. 8, No. 2, 469--513 (2002; Zbl 1005.35019)].
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93B18
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 1967716
zbMATH Keywords: controllability with respect to shape
zbMATH Keywords: elliptic equation
zbMATH Keywords: discretization
zbMATH Keywords: linearization
reviewed by: Wiesław Kotarski
MaRDI profile type: Publication
full work available at URL: s00211-002-0443-8
OpenAlex ID: W2031038466
DOI: 10.1007/S00211-002-0443-8
description: scientific article; zbMATH DE number 1967716