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2011 Interior Controllability of the Thermoelastic Plate Equation
H. Leiva, N. Merentes
Afr. Diaspora J. Math. (N.S.) 12(1): 46-59 (2011).


In this paper we prove the interior controllability of the Thermoelastic Plate Equation

$$ \left\{ \begin{array}{ll} w_{tt}+\Delta^2w+\alpha\Delta w=1_{\omega}u_{1}(t,x),& \mbox{in} \quad (0, \tau) \times \Omega,\\ \theta_t-\beta\Delta\theta-\alpha\Delta w_t=1_{\omega}u_{2}(t,x), & \mbox{in} \quad (0, \tau) \times \Omega,\\ \theta=w=\Delta w=0, & \mbox{on} \quad (0, \tau) \times \partial \Omega, \end{array} \right.$$

where $\alpha\neq 0$, $\beta>0$, $\Omega$ is a sufficiently regular bounded domain in $\R^{N}$ $(N\geq 1)$, $\omega$ is an open nonempty subset of $\Omega$, $1_{\omega}$ denotes the characteristic function of the set $\omega$ and the distributed control $u_{i}\in L^{2}([0,\tau]; L^{2}(\Omega)), i=1,2.$ Specifically, we prove the following statement: For all $\tau >0$ the system is approximately controllable on $[0, \tau]$. Moreover, we exhibit a sequence of controls steering the system from an initial state to a final state in a prefixed time $\tau >0$ .


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H. Leiva. N. Merentes . "Interior Controllability of the Thermoelastic Plate Equation." Afr. Diaspora J. Math. (N.S.) 12 (1) 46 - 59, 2011.


Published: 2011
First available in Project Euclid: 11 August 2011

zbMATH: 1243.93019
MathSciNet: MR2826841

Primary: 93B05 , 93C25

Keywords: interior controllability , strongly continuous semigroups , thermoelastic plate equation

Rights: Copyright © 2011 Mathematical Research Publishers

Vol.12 • No. 1 • 2011
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