Some stability results for timoshenko systems with cooperative frictional and infinite-memory dampings in the displacement

doi:10.1016/S0252-9602(15)30075-8

Acta Mathematica Scientia

Volume 36, Issue 1, January 2016, Pages 1-33

https://doi.org/10.1016/S0252-9602(15)30075-8 Get rights and content

Abstract

In this paper, we consider a vibrating system of Timoshenko-type in a one-dimensional bounded domain with complementary frictional damping and infinite memory acting on the transversal displacement. We show that the dissipation generated by these two complementary controls guarantees the stability of the system in case of the equal-speed propagation as well as in the opposite case. We establish in each case a general decay estimate of the solutions. In the particular case when the wave propagation speeds are different and the frictional damping is linear, we give a relationship between the smoothness of the initial data and the decay rate of the solutions. By the end of the paper, we discuss some applications to other Timoshenko-type systems.

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Some stability results for timoshenko systems with cooperative frictional and infinite-memory dampings in the displacement

Abstract

J Diff Equa

J Math Anal Appl

Appl Math Comput

Appl Math Comput

Nonl Anal: TMA

J Math Anal Appl

J Math Anal Appl

J Math Anal Appl

Nonl Anal

Appl Math Lett

J Diff Equ

J Diff Equ

Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control

Nonlinear Diff Equa Appl

Stability to weakly dissipative Timoshenko systems

Math Meth Appl Sci

Stability to 1-D thermoelastic Timoshenko beam acting on shear force

Z Angew Math Phys

Frictional versus viscoelastic damping in a semilinear wave equation

SIAM J Control and Optim

Asymptotic stability in viscoelasticity

Arch Rational Mech Anal

Stability of Timoshenko systems with past history

J Math Anal Appl

On the stability of damped Timoshenko systems: Cattaneo versus Fourier's law

Arch Rational Mech Anal