Exact boundary controllability on L2(Ω)×H−1(Ω) of the wave equation with Dirichlet boundary control acting on a portion of the boundary Ω, and related problems

2006 ◽  
pp. 292-332 ◽  
Author(s):  
R. Triggiani
Keyword(s):  
Wave Equation ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
Dirichlet Boundary Control ◽  
Exact Boundary

Exact controllability for a model of a multidimensional flexible structure

1993 ◽  
Vol 123 (2) ◽  
pp. 323-344 ◽  
Author(s):  
Jean Pierre Puel ◽  
Enrique Zuazua
Keyword(s):  
Wave Equation ◽  
Simple Model ◽  
Exact Controllability ◽  
Flexible Structure ◽  
Junction Region ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
One Dimensional ◽  
Exact Boundary ◽  
Simple Boundary

SynopsisA simple model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional straight string is introduced. In both regions (n-dimensional body and a onedimensional string) the state is assumed to satisfy the wave equation. Simple boundary conditions are introduced at the junction. These conditions, in the absence of control, ensure conservation of the total energy of the system and imply some rigidity of the boundary of the n-d body on a neighbourhood of the junction. The exact boundary controllability of the system is proved by means of a Dirichlet control supported on a subset of the boundary of the n-d domain which excludes the junction region. Some extensions are discussed at the end of the paper.

scholarly journals The operatorB*Lfor the wave equation with Dirichlet control

2004 ◽  
Vol 2004 (7) ◽  
pp. 625-634 ◽  
Author(s):  
I. Lasiecka ◽  
R. Triggiani
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Arbitrary Dimension ◽  
Energy Methods ◽  
Smooth Bounded Domain ◽  
Dirichlet Boundary Control

In the case of the wave equation, defined on a sufficiently smooth bounded domain of arbitrary dimension, and subject to Dirichlet boundary control, the operatorB*Lfrom boundary to boundary is bounded in theL2-sense. The proof combines hyperbolic differential energy methods with a microlocal elliptic component.

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