# Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity

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

- Volume: 3, page 23-48
- ISSN: 1292-8119

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topLiu, Weijiu. "Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 23-48. <http://eudml.org/doc/116568>.

@article{Liu2010,

abstract = {
The problem of partial exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity is
considered. By introducing a velocity feedback on part of the boundary of the thermoelastic body, which is clamped along the rest of its boundary, to
increase the loss of energy, we prove that the energy in the system of thermoelasticity decays to zero exponentially. We also give a positive answer to
a related open question raised by Alabau and Komornik for the Lamé system. Via Russell's “Controllability via Stabilizability" principle, we then
prove that the thermoelastic system is partially controllable with boundary controls without smallness restrictions on the coupling parameters.
},

author = {Liu, Weijiu},

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

keywords = {Partial exact controllability; exponential stability;
thermoelasticity. ; exact controllability; linear thermoelasticity; boundary control; velocity feedback},

language = {eng},

month = {3},

pages = {23-48},

publisher = {EDP Sciences},

title = {Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity},

url = {http://eudml.org/doc/116568},

volume = {3},

year = {2010},

}

TY - JOUR

AU - Liu, Weijiu

TI - Partial exact controllability and exponential stability in higher-dimensional linear thermoelasticity

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 3

SP - 23

EP - 48

AB -
The problem of partial exact boundary controllability and exponential stability for the higher-dimensional linear system of thermoelasticity is
considered. By introducing a velocity feedback on part of the boundary of the thermoelastic body, which is clamped along the rest of its boundary, to
increase the loss of energy, we prove that the energy in the system of thermoelasticity decays to zero exponentially. We also give a positive answer to
a related open question raised by Alabau and Komornik for the Lamé system. Via Russell's “Controllability via Stabilizability" principle, we then
prove that the thermoelastic system is partially controllable with boundary controls without smallness restrictions on the coupling parameters.

LA - eng

KW - Partial exact controllability; exponential stability;
thermoelasticity. ; exact controllability; linear thermoelasticity; boundary control; velocity feedback

UR - http://eudml.org/doc/116568

ER -

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