The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials
TLDR
In this paper, the controllability of a system of n one-dimensional parabolic equations with m control is proved. But the controLL of the system is restricted to a part of the boundary by means of m controls.About:
This article is published in Journal de Mathématiques Pures et Appliquées.The article was published on 2011-12-01 and is currently open access. It has received 85 citations till now. The article focuses on the topics: Biorthogonal system & Controllability.read more
Citations
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Journal ArticleDOI
Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
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Recent results on the controllability of linear coupled parabolic problems: a survey
TL;DR: In this paper, the authors summarize recent results on the controllability of parabolic systems of (several) parabolic equations, and the emphasis is placed on the extension of the Kalman rank condition (for finite dimensional systems of differing differential equations) to parabolic system.
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Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components
Jean-Michel Coron,Pierre Lissy +1 more
TL;DR: In this article, a local null controllability result for the three-dimensional Navier-Stokes equations on a (smooth) bounded domain with null Dirichlet boundary conditions was proved.
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Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components
Jean-Michel Coron,Pierre Lissy +1 more
TL;DR: In this paper, a local null controllability result for the three-dimensional Navier-Stokes equations on a (smooth) bounded domain of R^3 with null Dirichlet boundary conditions was proved.
Journal ArticleDOI
Minimal time for the null controllability of parabolic systems: The effect of the condensation index of complex sequences
TL;DR: In this paper, the existence of a minimal time T 0 ∈ [ 0, ∞ ] depending on Bernstein's condensation index of Λ and on B such that y = A y + B u is null-controllable at any time T > T 0 and not null-controlled for T T 0.
References
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Book
Real and complex analysis
TL;DR: In this paper, the Riesz representation theorem is used to describe the regularity properties of Borel measures and their relation to the Radon-Nikodym theorem of continuous functions.
Book
Observation and Control for Operator Semigroups
Marius Tucsnak,George Weiss +1 more
TL;DR: The main topics of interest about observation and control operators are admissibility, observability, controllability, stabilizability and detectability as discussed by the authors, which is a mature area of functional analysis, which is still very active.
Journal ArticleDOI
Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions
TL;DR: The current state of controllability and observability theories for linear PDEs is summarized in this article.However, the state of the art for observability and controllable PDE theories is limited.
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