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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 143-167. <http://eudml.org/doc/90643>.

@article{Belishev2010,

abstract = {
The boundary control problem for the dynamical Lame system
(isotropic elasticity model) is considered. The continuity of
the “input → state" map in L2-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
$\\{ u(\cdot ,T),u_t(\cdot ,T)\\}$
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 T0 exceeds the time needed
for shear waves to fill the entire domain, then the response
operator (“input → output" map) $R^\{2T_0\}$ uniquely determines
RT for any T>0. A procedure recovering R∞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.; isotropic elasticity; structure of sets reachable from the boundary in a short time; boundary controllability},

language = {eng},

month = {3},

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/90643},

volume = {8},

year = {2010},

}

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

DA - 2010/3//

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 → state" map in L2-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
$\{ u(\cdot ,T),u_t(\cdot ,T)\}$
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 T0 exceeds the time needed
for shear waves to fill the entire domain, then the response
operator (“input → output" map) $R^{2T_0}$ uniquely determines
RT for any T>0. A procedure recovering R∞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.; isotropic elasticity; structure of sets reachable from the boundary in a short time; boundary controllability

UR - http://eudml.org/doc/90643

ER -

## References

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