## Differential and Integral Equations

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

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

G. Perla Menzala and E. Zuazua

#### 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

**Permanent link to this document**

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