Displaying similar documents to “Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass”

Approximate controllability of linear parabolic equations in perforated domains

Patrizia Donato, Aïssam Nabil (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider an approximate controllability problem for linear parabolic equations with rapidly oscillating coefficients in a periodically perforated domain. The holes are ε -periodic and of size ε . We show that, as ε → 0 , the approximate control and the corresponding solution converge respectively to the approximate control and to the solution of the homogenized problem. In the limit problem, the approximation of the final state is alterated by a constant which depends on the...

Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations

Jean-Michel Coron (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.

Stabilization of second order evolution equations by a class of unbounded feedbacks

Kais Ammari, Marius Tucsnak (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.

Some new results related to the null controllability of the 1 - d heat equation

Antonio López, Enrique Zuazua (1997-1998)

Séminaire Équations aux dérivées partielles

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We address three null controllability problems related to the 1 - d heat equation. First we show that the 1 - d heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation...