Uniform decay rates for a nonlinear thermoelastic system

The uniform stability of a thermoelastic plate model is investigated, this model being described by a coupling of the dynamical Von Kármán and heat equations. Linear analogs of this work were considered in [1] and [2]. Even in the absence of inserted dissipative feedbacks on the boundary, we determine this system's stability with exponential decay rates which are uniform with respect to the crucial parameter γ described below (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [6], as was that of the analytic case γ = 0 in [11]); both the analytic and nonanalytic cases are treated here. The proof of this result involves a classical multiplier method, but with the particular multiplier being of a rather nonstandard (pseudodifferential) nature. Free use is also made of "sharp" regularity results for the Airy stress function which were recently derived in [4].