African Diaspora Journal of Mathematics

Interior Controllability of the Thermoelastic Plate Equation

H. Leiva and N. Merentes

Full-text: Open access

Abstract

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 $\tau >0$ .

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 12, Number 1 (2011), 46-59.

Dates
First available in Project Euclid: 11 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1313092841

Mathematical Reviews number (MathSciNet)
MR2826841

Zentralblatt MATH identifier
1243.93019

Subjects
Primary: 93B05: Controllability 93C25: Systems in abstract spaces

Keywords
interior controllability thermoelastic plate equation strongly continuous semigroups

Citation

Leiva, H.; Merentes , N. Interior Controllability of the Thermoelastic Plate Equation. Afr. Diaspora J. Math. (N.S.) 12 (2011), no. 1, 46--59. https://projecteuclid.org/euclid.adjm/1313092841


Export citation