A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods

1990 ◽  
Vol 7 (1) ◽  
pp. 1-76 ◽  
Author(s):  
Roland Glowinski ◽  
Chin-Hsien Li ◽  
Jacques-Louis Lions
Keyword(s):  
Wave Equation ◽  
Numerical Methods ◽  
Numerical Approach ◽  
Exact Boundary Controllability ◽  
Boundary Controllability ◽  
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.

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