Displaying similar documents to “The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation”

A singular perturbation problem in exact controllability of the Maxwell system

John E. Lagnese (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact controllability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the...

Exact controllability of the wave equation with mixed boundary condition and time-dependent coefficients

M. M. Cavalcanti (1999)

Archivum Mathematicum

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In this paper we study the boundary exact controllability for the equation ∂ ∂ t α ( t ) ∂ y ∂ t - ∑ j = 1 n ∂ ∂ x j β ( t ) a ( x ) ∂ y ∂ x j = 0 in Ω × ( 0 , T ) , when the control action is of Dirichlet-Neumann form and Ω is a bounded domain in R n . The result is obtained by applying the HUM (Hilbert Uniqueness Method) due to J. L. Lions.

How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance

George Weiss, Marius Tucsnak (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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Let A 0 be a possibly unbounded positive operator on the Hilbert space H , which is boundedly invertible. Let C 0 be a bounded operator from 𝒟 A 0 1 2 to another Hilbert space U . We prove that the system of equations z ¨ ( t ) + A 0 z ( t ) + 1 2 C 0 * C 0 z ˙ ( t ) = C 0 * u ( t ) y ( t ) = - C 0 z ˙ ( t ) + u ( t ) , determines a well-posed linear system with input u and output y . The state of this system is x ( t ) = z ( t ) z ˙ ( t ) ∈ 𝒟 A 0 1 2 × H = X , where X is the state space. Moreover, we have the energy identity ∥ x ( t ) ∥ X 2 - ∥ x ( 0 ) ∥ X 2 = ∫ 0 T ∥ u ( t ) ∥ U 2 d t - ∫ 0 T ∥ y ( t ) ∥ U 2 d t . We show that the system described...

Exact boundary controllability of a hybrid system of elasticity by the HUM method

Bopeng Rao (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.