|Publication ahead of print|
|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.
Corresponding author: email@example.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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