ON THE EQUIVALENCE OF MINIMAL TIME AND MINIMAL NORM CONTROLS FOR INTERNALLY CONTROLLED HEAT EQUATIONS

Wang G, Zuazua E (2012)

Publication Type: Journal article

Publication year: 2012

Journal

SIAM Journal on Control and Optimization Society for Industrial and Applied Mathematics

Book Volume: 50

Pages Range: 2938-2958

Journal Issue: 5

DOI: 10.1137/110857398

Abstract

We prove the equivalence of the minimal time and minimal norm control problems for heat equations on bounded smooth domains of the Euclidean space with homogeneous Dirichlet boundary conditions and controls distributed internally on an open subset of the domain where the equation evolves. We consider the problem of null controllability whose aim is to drive solutions to rest in a finite final time. As a consequence of this equivalence, using the well-known variational characterization of minimal norm controls we establish necessary and sufficient conditions for the minimal time and the corresponding control.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Wuhan University CN China (CN) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Wang, G., & Zuazua, E. (2012). ON THE EQUIVALENCE OF MINIMAL TIME AND MINIMAL NORM CONTROLS FOR INTERNALLY CONTROLLED HEAT EQUATIONS. SIAM Journal on Control and Optimization, 50(5), 2938-2958. https://dx.doi.org/10.1137/110857398

MLA:

Wang, Gengsheng, and Enrique Zuazua. "ON THE EQUIVALENCE OF MINIMAL TIME AND MINIMAL NORM CONTROLS FOR INTERNALLY CONTROLLED HEAT EQUATIONS." SIAM Journal on Control and Optimization 50.5 (2012): 2938-2958.

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