Differential and Integral Equations

Exact controllability of a thermoelastic system with control in the thermal component only

George Avalos

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Abstract

In this work we give a result of exact controllability for a thermoelastic system in which the control term is placed solely in the thermal equation. With such an indirect control input, one is able to control exactly the displacement of the plate, as well as the temperature. This exact controllability occurs in arbitrarily small time. In the case that the moment of inertia parameter for the plate is absent (i.e., $\gamma =0$ below), then one is provided here with a result of exact controllability for a thermoelastic system which is modelled by the generator of an analytic semigroup. The proof here depends upon a multiplier method so as to attain the associated observability inequality. The particular multiplier invoked is of an operator theoretic nature, and has been used previously by the author in deriving stability results for this partial differential equation model.

Article information

Source
Differential Integral Equations Volume 13, Number 4-6 (2000), 613-630.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061241

Mathematical Reviews number (MathSciNet)
MR1750042

Zentralblatt MATH identifier
0970.93002

Subjects
Primary: 93B05: Controllability
Secondary: 35B37 74F05: Thermal effects 74M05: Control, switches and devices ("smart materials") [See also 93Cxx] 93C20: Systems governed by partial differential equations

Citation

Avalos, George. Exact controllability of a thermoelastic system with control in the thermal component only. Differential Integral Equations 13 (2000), no. 4-6, 613--630. https://projecteuclid.org/euclid.die/1356061241.


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