Advances in Differential Equations

Exponential decay of Timoshenko systems with indefinite memory dissipation

Hugo D. Fernández Sare and Jaime E. Muñoz Rivera

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Abstract

We study the asymptotic behavior of Timoshenko systems with memory, where the memory is given by a non-dissipative kernel and is acting only on one equation of the system. We show that the exponential stability depends on conditions regarding the decay rate of the kernel and a nice relationship between the coefficients of the system. Moreover, with full-memory effect in the system, we will show exponential stability in the general case.

Article information

Source
Adv. Differential Equations Volume 13, Number 7-8 (2008), 733-752.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867334

Mathematical Reviews number (MathSciNet)
MR2479028

Zentralblatt MATH identifier
1173.35371

Subjects
Primary: 35Q74: PDEs in connection with mechanics of deformable solids
Secondary: 35B35: Stability 35B40: Asymptotic behavior of solutions 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 47N20: Applications to differential and integral equations

Citation

Muñoz Rivera, Jaime E.; Fernández Sare, Hugo D. Exponential decay of Timoshenko systems with indefinite memory dissipation. Adv. Differential Equations 13 (2008), no. 7-8, 733--752. https://projecteuclid.org/euclid.ade/1355867334.


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