| Issue |
ESAIM: COCV
Volume 24, Number 1, January-March 2018
|
|
|---|---|---|
| Page(s) | 289 - 309 | |
| DOI | https://doi.org/10.1051/cocv/2017009 | |
| Published online | 22 January 2018 | |
Estimates for the controls of the wave equation with a potential
1
Department of Mathematics, University of Craiova, 200585 and Institute of Mathematical Statistics and Applied Mathematics,
70700,
Bucharest, Romania
2
Department of Mathematics, University of Craiova,
200585, Romania
temereanca_laurentiu@yahoo.com
a Corresponding author: sd_micu@yahoo.com
Received:
17
March
2016
Accepted:
29
January
2017
This article studies the L2-norm of the boundary controls for the one dimensional linear wave equation with a space variable potential a = a(x). It is known these controls depend on a and their norms may increase exponentially with ||a||L∞. Our aim is to make a deeper study of this dependence in correlation with the properties of the initial data. The main result of the paper shows that the minimal L2−norm controls are uniformly bounded with respect to the potential a, if the initial data have only sufficiently high eigenmodes.
Mathematics Subject Classification: 93B05 / 30E05 / 42C15
Key words: Wave equation / boundary control / potential / moment problem / biorthogonals
© EDP Sciences, SMAI 2018
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