Abstract :
In this paper, we provide results of local and global null controllability for 2-D thermoelastic systems,
in the absence of rotational inertia, and under the influence of the (nonLipschitz) von Kármán
nonlinearity. The plate component may be taken to satisfy either the clamped or higher order (and
physically relevant) free boundary conditions. In the accompanying analysis, critical use is made of
sharp observability estimates which obtain for the linearization of the thermoelastic plate (these being
derived in [G. Avalos, I. Lasiecka, The null controllability of thermoelastic plates and singularity
of the associated minimal energy function, J. Math. Anal. Appl. 294 (2004) 34–61] and [G. Avalos,
I. Lasiecka, Asymptotic rates of blowup for the minimal energy function for the null controllability
of thermoelastic plates: The free case, in: Proc. of the Conference for the Control of Partial Differential
Equations, Georgetown University, Dekker, in press]). Moreover, another key ingredient in our
work to steer the given nonlinear dynamics is the recent result in [A. Favini, M.A. Horn, I. Lasiecka,
D. Tataru, Addendum to the paper: Global existence, uniqueness and regularity of solution to a von
Kármán system with nonlinear boundary dissipation, Differential Integral Equations 10 (1997) 197–
200] concerning the sharp regularity of the von Kármán nonlinearity.
2005 Elsevier Inc. All rights reserved
