Optimality on Polynomial decay of semigroups in Elasticity
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Optimality on Polynomial decay of semigroups in Elasticity By Jaime E. Muñoz Rivera LNCC IM-UFRJ. Our problem :. Given a semigroup of contractions T(t) defined over Hilbert space H, find the best number p such that. know result about Polynomial stability.

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Optimality on Polynomial decay of semigroups in Elasticity

By

Jaime E. Muñoz Rivera

LNCC

IM-UFRJ


Our problem:

Given a semigroup of contractions T(t) defined over Hilbert space H, find the best number p such that


knowresultabout

Polynomialstability






Pruss method give a necessary and a sufficient condition to prove polynomial estability

The problem is that it is not a simple task to estimate fractional powers of the operator of I.G.S.

It is more easy to deal with the sufficient condition given by Liu and Rao.

Our purporse is to show that the sufficient condition of Liu and Rao is also a necessary condition



This is a join work with Luci Fatori: given by a result due to

Estadual University of Londrina

Paraná – Brasil

e-mail: [email protected]

Our interest is to prove that the sufficient condition of Liu

and Rao is also a necessary condition.


Our main result is the following necessary condition given by a result due to

This result will be important to show when a rate of decay is optimal.

The proof is based on Pruss necessary condition and Latushkin –Shvidkoy result.


Aplications given by a result due to


The Infenitesimal generator of the semigroup is given by a result due to

We denote the associated semigroup as


Previous given by a result due toresult


That system was studied by Chen and Triggiani. They given by a result due to proved that the semigroup is analytic if

The authors solved the conjetures of G. Chen and D. L. Russel on structural damping for elastic systems.



Our when

Contribution


Our contribution is about polynomial stability for when

Our stability result to damped wave equation is


Idea whenoftheproofoftheoptimality:


Our when

contribution

to Bresse system


Thanks when


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