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The reachability problem for thermoelastic plates. (English) Zbl 0744.73028

In this paper, the boundary value problem which describes the small vibrations of a thin, homogeneous, isotropic, thermoelastic plate of uniform thickness is considered.
The reachability problem is defined as: \(R_ T=\{\{w(T),w'(T)\}\mid\{v_ 1,v_ 2\}\in{\mathcal S}\}\), where \(\mathcal S\) is a suitable space of controls.
According to the author, the main result of the present paper is that, in fact, the thermal effects do not affect the reachable set provided the thermal strains are sufficiently small. The paper is mathematically rigorous and is of use to practicing applied mathematicians.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
74A15 Thermodynamics in solid mechanics
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