On controllability of the Navier-Stokes equations

Fursikov, A. V.

doi:10.1007/978-3-0348-8689-5_6

Cited by 27 publications

(53 citation statements)

References 8 publications

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“…The controllability of the N -dimensional case, still for the scalar equation (n = 1), has been established later by G. Lebeau and L. Robbiano in [31] and by A. Fursikov and O. Yu. Imanuvilov in [22] using Carleman estimates. It is interesting to point out that the boundary and distributed null controllability of scalar parabolic problems is valid for any positive time T , for any Γ 0 ⊂ ∂Ω and for any ω ⊂ Ω.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence

Khodja

Benabdallah

González-Burgos

et al. 2016

Journal of Mathematical Analysis and Applications

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We consider the null controllability problem for two coupled parabolic equations with a space-depending coupling term. We analyze both boundary and distributed null controllability. In each case, we exhibit a minimal time of control, that is to say, a time T0 ∈ [0, ∞] such that the corresponding system is null controllable at any time T > T0 and is not if T < T0. In the distributed case, this minimal time depends on the relative position of the control interval and the support of the coupling term. We also prove that, for a fixed control interval and a time τ0 ∈ [0, ∞], there exist coupling terms such that the associated minimal time is τ0.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence

Khodja

Benabdallah

González-Burgos

et al. 2016

Journal of Mathematical Analysis and Applications

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“…When m = 1 (one equation and one control force) the null controllability of parabolic problems has been studied by several authors (see for instance [18], [17], [4], [10], ...). We also point out [14] and [15] where the null controllability of system (4) at time T was established for every…”

Section: Introductionmentioning

confidence: 99%

Controllability results for cascade systems of $m$ coupled parabolic PDEs by one control force

González-Burgos¹,

Teresa²

2010

Port. Math.

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Abstract.In this paper we will analyze the controllability properties of a linear coupled parabolic system of m equations when a unique distributed control is exerted on the system. We will see that, when a cascade system is considered, we can prove a global Carleman inequality for the adjoint system which bounds the global integrals of the variable ϕ = (ϕ1, . . . , ϕm)* in terms of a unique localized variable. As a consequence, we will obtain the null controllability property for the system with one control force. Mathematics Subject Classification (2000). 93B05, 93B07, 35K50.

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“…Imanuvilov en [5] con una hipótesis de mayor regularidad sobre el potencial b, más precisamente, ellos consideraron b i ∈ C 0,1 Q y utilizaron las desigualdades de Carleman en norma L 2 (Ω) para ecuaciones parabólicas. Cuando el potencial b i pertenece a L ∞ (Q) tales desigualdades no pueden ser utilizadas para concluir la controlabilidad nula del problema (2) -(3).…”

Section: Formulación Del Problemaunclassified

Control nulo para la ecuación lineal del calor sobre espacios con peso

Zannini

Ayala

2016

Pesquimat

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Resumen: En este trabajo estudiaremos la controlabilidad nula de la ecuación lineal del calor sobre espacios de Lebesgue y de Sobolev con peso. Dado el PVIF, en Ω demostraremos la existencia de un control u en espacios con peso que al actuar en el interior del dominio, conduce al sistema al equilibrio. La herramienta que usaremos para tal fin son las Desigualdades de Carleman.Palabras Claves: Controlabilidad nula, control interno, desigualdad de Carleman, espacios con peso. NULL CONTROLLABILITY OF THE LINEAR HEAT EQUATION ON THE WEIGHT SPACESAbstract: In this work, we study the null controllability of the linear heat equation on Lebesgue and Sobolev weight spaces. Given the initial and boundary value problemwe show the existence of a control function u belong to weight spaces that to acts on a subset of the domain Ω leads system to the equilibrium. The principal tool that we use is the Carleman´s inequality.Key Words: Null controllability, internal control, Carleman inequality, weight spaces. IntroducciónSea Ω un dominio acotado de R n , n ≥ 1, con frontera Γ = ∂Ω de clase C 2 . Consideremos la ecuación del calor

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On controllability of the Navier-Stokes equations

Cited by 27 publications

References 8 publications

New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence

New phenomena for the null controllability of parabolic systems: Minimal time and geometrical dependence

Controllability results for cascade systems of $m$ coupled parabolic PDEs by one control force

Control nulo para la ecuación lineal del calor sobre espacios con peso

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