Spike controls for elliptic and parabolic PDEs

Casas E, Zuazua E (2013)

Publication Type: Journal article

Publication year: 2013

Journal

Systems & Control Letters Elsevier

Book Volume: 62

Pages Range: 311-318

Journal Issue: 4

DOI: 10.1016/j.sysconle.2013.01.001

Abstract

We analyze the use of measures of the minimal norm to control elliptic and parabolic equations. We prove the sparsity of the optimal control. In the parabolic case, we prove that the solution of the optimization problem is a Borel measure supported in a set of Lebesgue measure zero. In both cases, the approximate controllability can be achieved efficiently by means of controls that are activated in some finite number of pointwise locations. We also analyze the corresponding dual problem. (C) 2013 Elsevier B.V. All rights reserved.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Universidad de Cantabria (UC) ES Spain (ES) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Casas, E., & Zuazua, E. (2013). Spike controls for elliptic and parabolic PDEs. Systems & Control Letters, 62(4), 311-318. https://doi.org/10.1016/j.sysconle.2013.01.001

MLA:

Casas, Eduardo, and Enrique Zuazua. "Spike controls for elliptic and parabolic PDEs." Systems & Control Letters 62.4 (2013): 311-318.

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