slide1
Download
Skip this Video
Download Presentation
Optimality on Polynomial decay of semigroups in Elasticity By Jaime E. Muñoz Rivera LNCC IM-UFRJ

Loading in 2 Seconds...

play fullscreen
1 / 42

Optimality on Polynomial decay of semigroups in Elasticity By Jaime E. Muñoz Rivera LNCC IM-UFRJ - PowerPoint PPT Presentation


  • 68 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Optimality on Polynomial decay of semigroups in Elasticity By Jaime E. Muñoz Rivera LNCC IM-UFRJ' - rasul


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2

Our problem:

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

slide4

knowresultabout

Polynomialstability

slide11

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

slide14

This is a join work with Luci Fatori:

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.

slide15

Our main result is the following necessary condition

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.

slide18

The Infenitesimal generator of the semigroup is

We denote the associated semigroup as

slide20

That system was studied by Chen and Triggiani. They 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.

slide22

Our

Contribution

slide23

Our contribution is about polynomial stability for

Our stability result to damped wave equation is

slide35

Our

contribution

to Bresse system

ad