Abstract
We consider the dynamical von K\'arm\'an system describing the nonlinear vibrations of a thin plate. We take into account thermal effects as well as a rotational inertia term in the system. Our main result states that the total energy of the system, $E (t)$, satisfies the following estimate: there exist $C>0$ and $\omega > 0$ such that $$ E (t) \le C e^{-\frac{\omega}{1+R^2}\; t} E(0)\qquad \hbox{ as } \qquad t \to +\infty $$ provided $E (0) \le R$ and this for any $R>0$. The result is proved by constructing a Lyapunov function which is a suitable perturbation of the energy of the system that satisfies a differential inequality leading to this decay estimate.
Citation
G. Perla Menzala. E. Zuazua. "Energy decay rates for the von Kármán system of thermoelastic plates." Differential Integral Equations 11 (5) 755 - 770, 1998. https://doi.org/10.57262/die/1367329669
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