Geodesic
Estimates for the controls of the wave equation with a potential
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 289-309

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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 ( 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 L 2 −norm controls are uniformly bounded with respect to the potential a , if the initial data have only sufficiently high eigenmodes.

DOI : 10.1051/cocv/2017009
Classification : 93B05, 30E05, 42C15
Keywords: Wave equation, boundary control, potential, moment problem, biorthogonals

Micu, Sorin 1 ; Temereancă, Laurenţiu Emanuel 1

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

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