Exact controllability of a system of coupled strings in parallel

Rajaram, Rajeev; Najafi, M.

doi:10.1080/00036811003627492

Cited by 8 publications

(8 citation statements)

References 11 publications

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“…Stabilization and controllability for systems coupled by linear wave equations in parallel can be found in papers [19,15,20] and [18]. Such systems of the quasi-linear case have not been considered.…”

Section: Introduction and Main Resultsmentioning

confidence: 98%

“…Controllability for coupled linear wave equations has been investigated by many authors, we refer the readers to [15][16][17][18][19][20], etc. There are few results in higher dimensions for nonlinear cases.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Remark 1.2. The system (1.27) is a linear system when a(y) = y and l = 1, which is discussed in [18].…”

Section: Example Consider the Controllability Problemmentioning

confidence: 99%

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Boundary controllability for the quasi-linear wave equations coupled in parallel

Deng

Yao

2011

Nonlinear Analysis: Theory, Methods & Applications

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Section: Introduction and Main Resultsmentioning

confidence: 98%

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Boundary controllability for the quasi-linear wave equations coupled in parallel

Deng

Yao

2011

Nonlinear Analysis: Theory, Methods & Applications

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“…In the present paper, we investigate the observability inequality on wave equations coupled in parallel. Coupled system of wave equations have been studied widely, see23–26. However, most of these literature consider the constant coefficient case.…”

Section: Introductionmentioning

confidence: 99%

Exact controllability of wave equations with variable coefficients coupled in parallel

Chai

2010

Asian Journal of Control

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In this paper, we investigate exact controllability for coupled wave equations which have variable coefficients principal part. Observability inequality is obtained by using Riemannian geometry method and Carleman estimates. Furthermore, the exact controllability result is established with Dirichlet boundary controls when T>T0, where the lower bound T0 for the control time T is different from that obtained in the constant coefficient principal part case. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

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“…Recently, by using the HUM of Lions [8], Rajaram and Najafi [12] studied the exact boundary controllability problem for the equations (1.4) in C ∞ domains of R n , n 2, with controls of Dirichlet type acting on Γ 1 .…”

mentioning

confidence: 99%

On exact boundary controllability for linearly coupled wave equations

Bastos

Spezamiglio

Raposo

2011

Journal of Mathematical Analysis and Applications

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In this paper we study exact boundary controllability for a system of two linear wave equations coupled by lower order terms. We obtain square integrable control of Neuman type for initial state with finite energy, in nonsmooth domains of the plane. PreliminariesLet Ω ⊂ R 2 be a bounded simply connected domain with piecewise C ∞ boundary ∂Ω. It is assumed that ∂Ω has no cuspid points and that Ω lays in one side of ∂Ω. We will refer to this type of domain as curvilinear polygon. The exterior unit normal vector η is defined almost everywhere in ∂Ω. Points of R 2 × R are denoted by (x 1 , x 2 , t), denotes the Laplacian operator in the spatial variable x = (x 1 , x 2 ) ∈ R 2 and subscripts are used for partial derivatives. Consider the systemwith T > 0, α, β, γ , δ real constants and ∂Ω = Γ 0 ∪ Γ 1 is a decomposition of the boundary where the parts Γ 0 and Γ 1 have disjoint interiors but their closure may have common isolated points. Many problems in structural dynamics are modeled by this type of system. For instance, the equations (1.2) describe the transverse free vibrations of an elastically connected double-membrane compound system. In this case u and v are the displacements of two vibrating membranes measured from their equilibrium positions. The coupling terms ±α(u − v) represent forces imposed by the coupling elastic layer. If the membranes are held fixed on the portion Γ 0 of the * Corresponding author.

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Exact controllability of a system of coupled strings in parallel

Cited by 8 publications

References 11 publications

Boundary controllability for the quasi-linear wave equations coupled in parallel

Boundary controllability for the quasi-linear wave equations coupled in parallel

Exact controllability of wave equations with variable coefficients coupled in parallel

On exact boundary controllability for linearly coupled wave equations

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