scholarly journals Exact Neumann boundary controllability for problems of transmission of the wave equation

1999 ◽  
Vol 41 (1) ◽  
pp. 125-139 ◽  
Author(s):  
WEIJIU LIU ◽  
GRAHAM H. WILLIAMS
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Exact Controllability ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Boundary Controllability ◽  
Hilbert Uniqueness Method ◽  
Uniqueness Method ◽  
Initial States

Using the Hilbert Uniqueness Method, we study the problem of exact controllability in Neumann boundary conditions for problems of transmission of the wave equation. We prove that this system is exactly controllable for all initial states in L2(Ω)×(H1(Ω))′.

scholarly journals Controllability for a Wave Equation with Moving Boundary

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Lizhi Cui ◽  
Libo Song
Keyword(s):  
Wave Equation ◽  
Dirichlet Boundary ◽  
Moving Boundary ◽  
Energy Estimates ◽  
Boundary Controllability ◽  
One Dimensional ◽  
Elastic String ◽  
Hilbert Uniqueness Method ◽  
Uniqueness Method ◽  
Dimensional Wave

We investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than1-1/e, by Hilbert uniqueness method, sidewise energy estimates method, and multiplier method, we get partial Dirichlet boundary controllability. Moreover, we will give a sharper estimate on controllability time that only depends on the speed of the moving endpoint.

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