On the Exact Controllability of the Wave Equation with Interior and Boundary Controls

2005 ◽  
Vol 125 (1) ◽  
pp. 19-35 ◽  
Author(s):  
A. T. Bui
Keyword(s):  
Wave Equation ◽  
Exact Controllability ◽  
Boundary Controls

scholarly journals Exact controllability for a semilinear wave equation with both interior and boundary controls

2005 ◽  
Vol 2005 (6) ◽  
pp. 619-637 ◽  
Author(s):  
Bui An Ton
Keyword(s):  
Wave Equation ◽  
Exact Controllability ◽  
Open Domain ◽  
Semilinear Wave Equation ◽  
Boundary Controls ◽  
Feedback Laws

The exact controllability of a semilinear wave equation in a bounded open domain ofRn, with controls on a part of the boundary and in the interior, is shown. Feedback laws are established.

SOLUTION OF TIME-PERIODIC WAVE EQUATION USING MIXED FINITE ELEMENTS AND CONTROLLABILITY TECHNIQUES

2011 ◽  
Vol 19 (04) ◽  
pp. 335-352 ◽  
Author(s):  
SAMI KÄHKÖNEN ◽  
ROLAND GLOWINSKI ◽  
TUOMO ROSSI ◽  
RAINO A. E. MÄKINEN
Keyword(s):  
Periodic Solution ◽  
Wave Equation ◽  
Mixed Finite Elements ◽  
Exact Controllability ◽  
Periodic Wave ◽  
Mixed Formulation ◽  
Absorbing Boundary ◽  
Integrable Functions ◽  
Time Harmonic ◽  
Time Periodic

We consider a controllability method for the time-periodic solution of the two-dimensional scalar wave equation with a first order absorbing boundary condition describing the scattering of a time-harmonic incident wave by a sound-soft obstacle. Solution of the time-harmonic equation is equivalent to finding a periodic solution for the corresponding time-dependent wave equation. We formulate the problem as an exact controllability one and solve the wave equation in time-domain. In a mixed formulation we look for solutions u = (v, p)T. The use of mixed formulation allows us to set the related controllability problem in (L2(Ω))d+1, a space of square-integrable functions in dimension d + 1. No preconditioning is needed when solving this with conjugate gradient method. We present numerical results concerning performance and convergence properties of the method.

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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