Volume 24, Number 1, January-March 2018
|Page(s)||289 - 309|
|Published online||22 January 2018|
Estimates for the controls of the wave equation with a potential
Department of Mathematics, University of Craiova, 200585 and Institute of Mathematical Statistics and Applied Mathematics,
2 Department of Mathematics, University of Craiova, 200585, Romania
a Corresponding author: firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.