# 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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 36, Issue: 4, page 657-691
- ISSN: 0764-583X

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topPerla Menzala, G., Pazoto, Ademir F., and Zuazua, Enrique. "Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates." ESAIM: Mathematical Modelling and Numerical Analysis 36.4 (2010): 657-691. <http://eudml.org/doc/194120>.

@article{PerlaMenzala2010,

abstract = {
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
for which the energy tends to zero exponentially
as well. This is done both in the case of
internal and boundary damping. We address the same
problem for plates with internal damping.
},

author = {Perla Menzala, G., Pazoto, Ademir F., Zuazua, Enrique},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Uniform stabilization; singular limit; von Kármán system; beams; plates.; uniform stabilization},

language = {eng},

month = {3},

number = {4},

pages = {657-691},

publisher = {EDP Sciences},

title = {Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates},

url = {http://eudml.org/doc/194120},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Perla Menzala, G.

AU - Pazoto, Ademir F.

AU - Zuazua, Enrique

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 4

SP - 657

EP - 691

AB -
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
for which the energy tends to zero exponentially
as well. This is done both in the case of
internal and boundary damping. We address the same
problem for plates with internal damping.

LA - eng

KW - Uniform stabilization; singular limit; von Kármán system; beams; plates.; uniform stabilization

UR - http://eudml.org/doc/194120

ER -

## References

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