Spike controls for elliptic and parabolic PDEs
type: Item
instance of: scholarly article
title: Spike controls for elliptic and parabolic PDEs
zbMATH Open document ID: 1267.49005
author: Eduardo Casas
author: Enrique Zuazua
published in: Systems \& Control Letters
publication date: 2013-04-25T00:00:00Z
full work available at URL: http://hdl.handle.net/20.500.11824/565
review text: The authors use measures of minimal norm to control elliptic and parabolic equations. They show the sparsity of the optimal control. In the parabolic case they show that the solution of the optimization problem is a Borel measure supported in a set of null Lebesgue measure. ``In both cases, approximate controllability can be achieved efficiently by means of controls that are activated in some finite number of pointwise locations'' (from the abstract). The corresponding dual problems are also studied. Possible extensions of the obtained results and some open problems are pointed out.
reviewed by: Wiesław Kotarski
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49J30
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 6157692
zbMATH Keywords: parabolic equations
zbMATH Keywords: elliptic equations
zbMATH Keywords: approximate controllability
zbMATH Keywords: spike controls
zbMATH Keywords: Borel measures
MaRDI profile type: Publication
OpenAlex ID: W2015783980
DOI: 10.1016/J.SYSCONLE.2013.01.001
Recommended article: Stabilization by Sparse Controls for a Class of Semilinear Parabolic Equations
Recommended article: Approximation of Sparse Controls in Semilinear Elliptic Equations
Recommended article: Parabolic Control Problems in Measure Spaces with Sparse Solutions
Recommended article: Q5269453
Recommended article: Controllability of parabolic equations
Recommended article: Controllability and stabilization of parabolic equations
Recommended article: Control of Partial Differential Equations
Recommended article: Optimal Control of Nonlinear Elliptic Problems with Sparsity
Recommended article: Analysis of Spatio-Temporally Sparse Optimal Control Problems of Semilinear Parabolic Equations
Recommended article: Q4841088
description: scientific article; zbMATH DE number 6157692