On the stabilization of linear porous elastic materials by microtemperature effect and porous damping

Dridi, Hanni; Djebabla, Abdelhak

doi:10.1007/s11565-019-00333-2

Cited by 22 publications

(12 citation statements)

References 22 publications

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“…Apalara [4] considered this case for porous-elastic system and proved that the dissipation given only with the microtemperatures is sufficient to get an exponential stability for the case of equal speeds of wave propagation. In [17,26,35,36], the authors studied the porous thermoelastic system in case of zero thermal conductivity with temperatures and microtemperatures effects. They proved that the unique dissipation due to the microtemperatures is strong enough to make the energy of the considered systems decay to zero in an exponential manner without any condition on the coefficients of the system.…”

Section: Case Without Thermal Conductivitymentioning

confidence: 99%

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Decay in full von Kármán beam with temperature and microtemperatures effects

Aouadi

Guerine

2023

Math. Model. Nat. Phenom.

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In this article we derive the equations that constitute the mathematical model of the full von K\'{a}rm\'{a}n beam with temperature and microtemperatures effects. The nonlinear governing equations are derived by using Hamilton principle in the framework of Euler–Bernoulli beam theory. Under quite general assumptions on nonlinear damping function acting on the transversal component and based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions to the derived problem. Then using the multiplier method, we show that solutions decay exponentially. Finally we consider the case of zero thermal conductivity and we show that the dissipation given only by the microtemperatures is strong enough to produce exponential stability.

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Section: Case Without Thermal Conductivitymentioning

confidence: 99%

“…In this case, we show that the single dissipation due to microtemperatures is strong enough to exponentially stabilize the system without adding damping terms. So far, this case has only been considered for porous thermoelastic materials in [4,17,26,35,36].…”

Section: Introductionmentioning

confidence: 99%

Decay in full von Kármán beam with temperature and microtemperatures effects

Aouadi

Guerine

2023

Math. Model. Nat. Phenom.

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“…[7]. Although there is a good amount of literature dealing with stabilization of solutions for these systems (see for example [9], [16], [20], [22], [23], [26]), we did not find any works considering controllability for porous elastic systems.…”

Section: Introductionmentioning

confidence: 77%

Boundary exact controllability for a porous elastic Timoshenko system

Santos¹,

Raposo²,

Rodrigues³

2020

Appl.Math.

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“…The basic evolution equations for one-dimensional theories of swelling porous materials with temperature and microtemperature [25][26][27][28] are given by…”

Section: Introductionmentioning

confidence: 99%