This article studies the ${L}^{2}$-norm of the boundary controls for the one dimensional linear wave equation with a space variable potential $a=a\left(x\right)$. It is known these controls depend on $a$ and their norms may increase exponentially with $\u2225a\u2225{\phantom{\rule{0.166667em}{0ex}}}_{{L}^{\infty}}$. 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 ${L}^{2}$^{}−norm controls are uniformly bounded with respect to the potential $a$, if the initial data have only sufficiently high eigenmodes.

Keywords: Wave equation, boundary control, potential, moment problem, biorthogonals

^{1}; Temereancă, Laurenţiu Emanuel

^{1}

@article{COCV_2018__24_1_289_0, author = {Micu, Sorin and Temereanc\u{a}, Lauren\c{t}iu Emanuel}, title = {Estimates for the controls of the wave equation with a potential}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {289--309}, publisher = {EDP-Sciences}, volume = {24}, number = {1}, year = {2018}, doi = {10.1051/cocv/2017009}, mrnumber = {3843186}, zbl = {1396.93025}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017009/} }

TY - JOUR AU - Micu, Sorin AU - Temereancă, Laurenţiu Emanuel TI - Estimates for the controls of the wave equation with a potential JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 289 EP - 309 VL - 24 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017009/ DO - 10.1051/cocv/2017009 LA - en ID - COCV_2018__24_1_289_0 ER -

%0 Journal Article %A Micu, Sorin %A Temereancă, Laurenţiu Emanuel %T Estimates for the controls of the wave equation with a potential %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 289-309 %V 24 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017009/ %R 10.1051/cocv/2017009 %G en %F COCV_2018__24_1_289_0

Micu, Sorin; Temereancă, Laurenţiu Emanuel. Estimates for the controls of the wave equation with a potential. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 1, pp. 289-309. doi : 10.1051/cocv/2017009. http://archive.numdam.org/articles/10.1051/cocv/2017009/

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