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1998 Energy decay rates for the von Kármán system of thermoelastic plates
G. Perla Menzala, E. Zuazua
Differential Integral Equations 11(5): 755-770 (1998).

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

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G. Perla Menzala. E. Zuazua. "Energy decay rates for the von Kármán system of thermoelastic plates." Differential Integral Equations 11 (5) 755 - 770, 1998.

Information

Published: 1998
First available in Project Euclid: 30 April 2013

zbMATH: 1008.35077
MathSciNet: MR1666187

Subjects:
Primary: 35Q72
Secondary: 73B30, 73K10

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.11 • No. 5 • 1998
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