Exact controllability for the semilinear string equation in non cylindrical domains

F. Araruna; G. Antunes; L. Medeiros

Displaying similar documents to “Exact controllability for the semilinear string equation in non cylindrical domains”

Global controllability properties for the semilinear heat equation with superlinear term.

A. Y. Khapalov (1999)

Revista Matemática Complutense

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We discuss several global approximate controllability properties for the semilinear heat equation with superlinear reaction-convection term, governed in a bounded domain by locally distributed controls. First, based on the asymptotic analysis in vanishing time, we study the steering of the projections of its solution on any finite dimensional space spanned by the eigenfunctions for the truncated linear part. We show that, if the control-supporting area is properly chosen, then they...

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Subalakshmi, Ravikumar, Balachandran, Krishnan (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Exact controllability for semilinear wave equations in one space dimension

E. Zuazua (1993)

Annales de l'I.H.P. Analyse non linéaire

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Exact Neumann boundary controllability for second order hyperbolic equations

Weijiu Liu, Graham Williams (1998)

Colloquium Mathematicae

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Using HUM, we study the problem of exact controllability with Neumann boundary conditions for second order hyperbolic equations. We prove that these systems are exactly controllable for all initial states in $L^{2} (Ω) \times {(H^{1} (Ω))}^{'}$ and we derive estimates for the control time T.

Controllability of analytic functions for a wave equation coupled with a beam.

Brice Allibert, Sorin Micu (1999)

Revista Matemática Iberoamericana

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We consider the controllability and observation problem for a simple model describing the interaction between a fluid and a beam. For this model, microlocal propagation of singularities proves that the space of controlled functions is smaller that the energy space. We use spectral properties and an explicit construction of biorthogonal sequences to show that analytic functions can be controlled within finite time. We also give an estimate for this time, related to the amount of analyticity...

Exact controllability of a pluridimensional coupled problem.

Serge Nicaise (1992)

Revista Matemática de la Universidad Complutense de Madrid

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We set a coupled boundary value problem between two domains of different dimension. The first one is the unit cube of Rn, n C [2,3], with a crack and the second one is the crack. this problem comes from Ciarlet et al. (1989), that obtained an analogous coupled problem. We show that the solution has singularities due to the crack. As in Grisvard (1989), we adapt the Hilbert uniqueness method of J.-L. Lions (1968,1988) in order to obtain the exact controllability of the associated wave...

Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin, Marius Tucsnak (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.