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Stabilization of Berger–Timoshenko’s equation as limit of the uniform stabilization of the von Kármán system of beams and plates

G. Perla Menzala;  Ademir F. Pazoto;  Enrique Zuazua — 2002

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter ε > 0 and study its asymptotic behavior for t large, as ε → 0 . Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter ε . In order for this to be true the damping mechanism has to have the appropriate scale with respect to ε . In the limit as ε → 0 we obtain damped Berger–Timoshenko beam models...

Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates

G. Perla Menzala;  Ademir F. Pazoto;  Enrique Zuazua — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter ε > 0 and study its asymptotic behavior for large, as ε → 0. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter ε. In order for this to be true the damping mechanism has to have the appropriate scale with respect to ε. In the limit as ε → 0 we obtain damped Berger–Timoshenko...

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