# The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 8, page 143-167
- ISSN: 1292-8119

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topBelishev, M. I., and Lasiecka, I.. "The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 143-167. <http://eudml.org/doc/245575>.

@article{Belishev2002,

abstract = {The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input $\rightarrow $ state” map in $L_2$-norms is established. A structure of the reachable sets for arbitrary $T>0$ is studied. In general case, only the first component $u(\cdot ,T)$ of the complete state $\lbrace u(\cdot ,T),u_t(\cdot ,T)\rbrace $ may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation. If $T_0$ exceeds the time needed for shear waves to fill the entire domain, then the response operator (“input $\rightarrow $ output” map) $R^\{2T_0\}$ uniquely determines $R^T$ for any $T>0$. A procedure recovering $R^\infty $ via $R^\{2T_0\}$ is also described.},

author = {Belishev, M. I., Lasiecka, I.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {isotropic elasticity; dynamical Lame system; regularity of solutions; structure of sets reachable from the boundary in a short time; boundary controllability},

language = {eng},

pages = {143-167},

publisher = {EDP-Sciences},

title = {The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation},

url = {http://eudml.org/doc/245575},

volume = {8},

year = {2002},

}

TY - JOUR

AU - Belishev, M. I.

AU - Lasiecka, I.

TI - The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 8

SP - 143

EP - 167

AB - The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input $\rightarrow $ state” map in $L_2$-norms is established. A structure of the reachable sets for arbitrary $T>0$ is studied. In general case, only the first component $u(\cdot ,T)$ of the complete state $\lbrace u(\cdot ,T),u_t(\cdot ,T)\rbrace $ may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation. If $T_0$ exceeds the time needed for shear waves to fill the entire domain, then the response operator (“input $\rightarrow $ output” map) $R^{2T_0}$ uniquely determines $R^T$ for any $T>0$. A procedure recovering $R^\infty $ via $R^{2T_0}$ is also described.

LA - eng

KW - isotropic elasticity; dynamical Lame system; regularity of solutions; structure of sets reachable from the boundary in a short time; boundary controllability

UR - http://eudml.org/doc/245575

ER -

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