## Differential and Integral Equations

### Energy decay rates for the von Kármán system of thermoelastic plates

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 11, Number 5 (1998), 755-770.

Dates
First available in Project Euclid: 30 April 2013

https://projecteuclid.org/euclid.die/1367329669

Mathematical Reviews number (MathSciNet)
MR1666187

Zentralblatt MATH identifier
1008.35077

Subjects
Primary: 35Q72
Secondary: 73B30 73K10

#### Citation

Perla Menzala, G.; Zuazua, E. Energy decay rates for the von Kármán system of thermoelastic plates. Differential Integral Equations 11 (1998), no. 5, 755--770. https://projecteuclid.org/euclid.die/1367329669