A general stability result in a memory-type Timoshenko system

In this paper we consider the initial value problem for the Timoshenko system with a memory term. We construct the fundamental solution by using the Fourier–Laplace transform and obtain the solution formula of the problem. Moreover, applying the energy method in the Fourier space, we derive the pointwise estimate of solutions in the Fourier space, which gives a sharp decay estimate of solutions. It is shown that the decay property of the system is of the regularity-loss type and is weaker than that of the Timoshenko system with a frictional dissipation.

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General stability of memory-type thermoelastic Timoshenko beam acting on shear force

Continuum Mechanics and Thermodynamics ◽

10.1007/s00161-017-0601-y ◽

2017 ◽

Vol 30 (2) ◽

pp. 291-300 ◽

Cited By ~ 6

Author(s):

Tijani A. Apalara

Keyword(s):

Timoshenko Beam ◽

Shear Force ◽

General Stability ◽

Memory Type

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A general stability result for swelling porous elastic media with nonlinear damping

Applicable Analysis ◽

10.1080/00036811.2021.1979218 ◽

2021 ◽

pp. 1-16

Author(s):

T. Apalara ◽

A. Soufyane ◽

M. Afilal ◽

M. Alahyane

Keyword(s):

Stability Result ◽

Nonlinear Damping ◽

Elastic Media ◽

General Stability

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A stability result of a Timoshenko system in thermoelasticity of second sound with a delay term in the internal feedback

Georgian Mathematical Journal ◽

10.1515/gmj-2014-0045 ◽

2014 ◽

Vol 21 (4) ◽

Author(s):

Djamel Ouchenane

Keyword(s):

Heat Conduction ◽

Stability Result ◽

Well Posedness ◽

Second Sound ◽

Timoshenko System ◽

Wave Speeds ◽

One Dimensional ◽

Delay Term ◽

Semigroup Method ◽

Cattaneo’S Law

AbstractIn this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay term in the feedback. The heat conduction is given by Cattaneo's law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem. Furthermore, an exponential stability result is shown without the usual assumption on the wave speeds. To achieve our goals, we make use of the semigroup method and the energy method.

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Memory-type boundary control of a laminated Timoshenko beam

Mathematics and Mechanics of Solids ◽

10.1177/1081286520911078 ◽

2020 ◽

Vol 25 (8) ◽

pp. 1568-1588 ◽

Cited By ~ 1

Author(s):

Baowei Feng ◽

Abdelaziz Soufyane

Keyword(s):

Boundary Conditions ◽

Timoshenko Beam ◽

Stability Result ◽

Kernel Functions ◽

The Other ◽

Interfacial Slip ◽

Small Thickness ◽

Memory Type ◽

Type Boundary ◽

The Stability

In this paper, we consider a laminated Timoshenko beam with boundary conditions of a memory type. This structure is given by two identical uniform layers, one on top of the other, taking into account that an adhesive of small thickness bonds the two surfaces and produces an interfacial slip. Under the assumptions of wider classes of kernel functions, we establish an optimal explicit energy decay result. The stability result is more general than previous works and hence improves earlier results in the literature.

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