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Mechanical and thermal null controllability of thermoelastic plates and singularity of the associated mimimal energy function

Avalos G., Lasiecka I.

Control and Cybernetics

2003

Vol. 32, no 3

473-490

The null controllability problem is considered for 2-D thermoelastic plates under hinged mechanical boundary conditions. The resulting partial differential equation system generates an analytic semigroup on the space of finite energy. Consequently, because the thermoelastic system is associated with an infinite speed of propagation, the null controllability question is a suitable one for contemplation. It is shown that all finite energy states can be driven to zero by means of L^2(Q)-mechanical or thermal controls. In addition, the singularity of the minimal energy function, as T | 0, is also investigated. Ultimately, we establish the optimal blowup rate O(T-5/2) for this function, in the case one control (either mechanical or thermal ) is acting upon the system and O(T-5/2). in the case of two controls (thermal and mechanical). This rate of singularity is optimal and in fact the same as obtained by considering finite dimensional truncations of the thermoelastic PDE.

Uniform decay rates for solutions to a structural acoustics model with nonlinear dissipation

Avalos G., Lasiecka I.

Applied Mathematics and Computer Science

1998

Vol. 8, no 2

287-312

In this work, the asymptotic behavior of solutions to a coupled hyperbolic/parabolic-like system is investigated. It is shown that with both components of the equation being subjected to nonlinear damping (boundary damping for the wave component, interior for the beam), a global uniform stability is attained for all (weak) solutions.