no. 1
Exact controllability of the 1-d wave equation from a moving interior point
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 301-316.

We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.

DOI : 10.1051/cocv/2012009
Classification : 93B05, 93B07, 35L05
Mots clés : exact controllability, wave equation, pointwise control 
@article{COCV_2013__19_1_301_0,
     author = {Castro, Carlos},
     title = {Exact controllability of the 1-d wave equation from a moving interior point},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {301--316},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {1},
     year = {2013},
     doi = {10.1051/cocv/2012009},
     mrnumber = {3023072},
     zbl = {1258.93022},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2012009/}
}
TY  - JOUR
AU  - Castro, Carlos
TI  - Exact controllability of the 1-d wave equation from a moving interior point
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2013
SP  - 301
EP  - 316
VL  - 19
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv/2012009/
DO  - 10.1051/cocv/2012009
LA  - en
ID  - COCV_2013__19_1_301_0
ER  - 
%0 Journal Article
%A Castro, Carlos
%T Exact controllability of the 1-d wave equation from a moving interior point
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2013
%P 301-316
%V 19
%N 1
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv/2012009/
%R 10.1051/cocv/2012009
%G en
%F COCV_2013__19_1_301_0
Castro, Carlos. Exact controllability of the 1-d wave equation from a moving interior point. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 301-316. doi : 10.1051/cocv/2012009. http://www.numdam.org/articles/10.1051/cocv/2012009/

[1] S. Avdonin and S. Ivanov, Families of exponentials : The method of moments in controllability problems for distributed paramenter systems. Cambridge University Press (1995). | MR | Zbl

[2] A. Bamberger, J. Jaffre and J.P. Yvon, Punctual control of a vibrating string : Numerical analysis. Comput. Maths. Appl. 4 (1978) 113-138. | MR | Zbl

[3] C. Castro, Boundary controllability of the one-dimensional wave equation with rapidly oscillating density. Asymptotic Analysis 20 (1999) 317-350. | MR | Zbl

[4] C. Castro and E. Zuazua, Unique continuation and control for the heat equation from a lower dimensional manifold. SIAM J. Control. Optim. 42 (2005) 1400-1434. | MR | Zbl

[5] R. Dáger and E. Zuazua, Wave propagation observation and control in 1-d flexible multi-structures. Math. Appl. 50 (2006). | Zbl

[6] S. Hansen and E. Zuazua, Exact controllability and stabilization of a vibrating string with an interior point mass. SIAM J. Control Optim. 33 (1995) 1357-1391. | MR | Zbl

[7] A. Khapalov, Controllability of the wave equation with moving point control. Appl. Math. Optim. 31 (1995) 155-175. | MR | Zbl

[8] A. Khapalov, Mobile point controls versus locally distributed ones for the controllability of the semilinear parabolic equation. SIAM J. Contol. Optim. 40 (2001) 231-252. | MR | Zbl

[9] A. Khapalov, Observability and stabilization of the vibrating string equipped with bouncing point sensors and actuators. Math. Meth. Appl. Sci. 44 (2001) 1055-1072. | MR | Zbl

[10] J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications I. Springer-Verlag (1972). | MR | Zbl

[11] J.-L. Lions, Some methods in the mathematical analysis of systems and their control. Gordon and Breach (1981). | MR | Zbl

[12] J.-L. Lions, Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués. RMA 8 and 9, Tomes 1 and 2, Masson, Paris (1988). | MR | Zbl

[13] J.-L. Lions, Pointwise control for distributed systems, in Control and estimation in distributed parameter systems, edited by H.T. Banks. SIAM (1992). | MR | Zbl

Cité par Sources :