Stability results of locally coupled wave equations with local Kelvin-Voigt damping: Cases when the supports of damping and coupling coefficients are disjoint

Akil, Mohammad; Badawi, Haidar; Nicaise, Serge

doi:10.1007/s40314-022-01956-6

Cited by 9 publications

(14 citation statements)

References 24 publications

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“…The authors showed that the semigroup associated with a one-dimensional wave equation equipped with a local Kelvin-Voigt damping is not exponentially stable even when the damping is on the half of the domain. Speaking about Kelvin-Voigt damping, we mention also these works [15][16][17] and the references therein.…”

Section: Previous Literaturementioning

confidence: 99%

Exponential stability result for the wave equation with Kelvin–Voigt damping and past history subject to Wentzell boundary condition and delay term

Kechiche,

Khemmoudj,

Medjden

2023

Math Methods in App Sciences

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In this paper, we present an analysis of stability of solutions corresponding to a variable coefficient's wave equation subject to a locally Kelvin–Voigt damping and distributed effect driven by a nonnegative function with dynamic Wentzell boundary conditions and delay term. By using frequency domain approach method, we show that under a suitable assumption between the internal damping function and the boundary delay feedback, considering some geometrical assumptions on the boundary of , supposing that the relaxation function decay exponentially to zero, that the energies of the problem decay exponentially to zero.

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Section: Previous Literaturementioning

confidence: 99%

Exponential stability result for the wave equation with Kelvin–Voigt damping and past history subject to Wentzell boundary condition and delay term

Kechiche,

Khemmoudj,

Medjden

2023

Math Methods in App Sciences

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“…For this reason, the theory of indirect stabilization for coupled wave equations has been investigated extensively. See, in particular [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32] and the rich references therein. We also refer to the two monographs [33] and [34] for a comprehensive review.…”

Section: Introductionmentioning

confidence: 99%

Indirect boundary stabilization of strongly coupled degenerate hyperbolic systems

Salhi

Moumni

Tilioua

2023

Preprint

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In this paper, we consider the energy decay of a damped hyperbolic system of two degenerate wave equations coupled by velocities when only one equation is directly damped by a linear boundary feedback. To this aim, we first prove that the proposed system is well-posed using the semigroup theory. Then, under the hypothesis that the coupling coefficient is positive and small, we show that the total energy of the whole system decays exponentially. The explicit energy decay rate is established by using the energy multiplier method. MSC 2020: 35B40, 35L80, 93D15, 93D23

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“…Russell [5] first presented the concept of indirect stabilization, which means that just one equation of the coupled system is damped, and since that, it has been an interest of many authors (please see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Exponential stability and exact controllability of a system of coupled wave equations by second‐order terms (via Laplacian) with only one non‐smooth local damping

Akil,

Hajjej

2023

Math Methods in App Sciences

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The purpose of this work is to investigate the exponential stability of a second‐order coupled wave equations by Laplacian with one locally internal viscous damping. The strong stability is established by combining a unique continuation result and a Carleman estimate. Besides, the exponential stability is proved under (PMGC) condition on the damping region without any restriction on wave propagation speed (i.e., whether the two wave equations propagate at the same speed or not). The proof of this result relies on the frequency domain method combined with the multiplier techniques.

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Stability results of locally coupled wave equations with local Kelvin-Voigt damping: Cases when the supports of damping and coupling coefficients are disjoint

Cited by 9 publications

References 24 publications

Exponential stability result for the wave equation with Kelvin–Voigt damping and past history subject to Wentzell boundary condition and delay term

Exponential stability result for the wave equation with Kelvin–Voigt damping and past history subject to Wentzell boundary condition and delay term

Indirect boundary stabilization of strongly coupled degenerate hyperbolic systems

Exponential stability and exact controllability of a system of coupled wave equations by second‐order terms (via Laplacian) with only one non‐smooth local damping

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