Arched beams of Bresse type: observability and application in thermoelasticity

Moraes, Gabriel E. Bittencourt; Silva, Marcio A. Jorge

doi:10.1007/s11071-021-06243-3

Cited by 6 publications

(1 citation statement)

References 20 publications

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“…In this context, we have tried to evaluate the optimality by adapting the contradiction argument based on Borichev-Tomilov condition for the considered fractional Bresse system. But unfortunately, we were not able to construct the sequences of complex numbers (λ n ) n∈N and solutions [16,15,35]. Besides, we could not find appropriate references dealing with the decay rate optimality of fractional Bresse systems, which may reflect the intractability of such aspect.…”

Section: Now We Multiply the Equation λρmentioning

confidence: 98%

On the asymptotic stability of a Bresse system with two fractional damping terms: Theoretical and numerical analysis

Bentrcia

Mennouni

2023

DCDS-B

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<p style='text-indent:20px;'>The aim of this work is to investigate the asymptotic stability of a viscoelastic Bresse system in one dimensional bounded domain. In this context, we introduce two internal damping terms expressed using the generalized Caputo fractional derivative. By adopting a diffusive representation, we show the well-posedness of the proposed system and we prove some decay results. In order to validate the theoretical findings, we implement a finite difference method and we conduct intensive numerical simulations. Moreover, we provide some insights on the convergence of the elaborated numerical scheme.</p>

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Section: Now We Multiply the Equation λρmentioning

confidence: 98%

On the asymptotic stability of a Bresse system with two fractional damping terms: Theoretical and numerical analysis

Bentrcia

Mennouni

2023

DCDS-B

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Attractors of a thermoelastic Bresse system with mass diffusion

Li,

Cabanillas,

Feng

2024

Z Angew Math Mech

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This paper concerns the long‐time dynamics of a thermoelastic Bresse system with mass diffusion. We prove the existence of a global attractor by showing that the system is gradient and asymptotically smooth. In addition, the attractor is characterized as an unstable manifold of the set of stationary solutions. The quasi‐stability of the system and the finite fractal dimension of the global attractor are established by a stabilizability inequality. Finally, we prove the upper semicontinuity of the global attractor regarding the parameter in a dense residual set.

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Exponential Stability for a Bresse System with Hybrid Dissipation

Araújo

2023

Acta Appl Math

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Arched beams of Bresse type: observability and application in thermoelasticity

Cited by 6 publications

References 20 publications

On the asymptotic stability of a Bresse system with two fractional damping terms: Theoretical and numerical analysis

On the asymptotic stability of a Bresse system with two fractional damping terms: Theoretical and numerical analysis

Attractors of a thermoelastic Bresse system with mass diffusion

Exponential Stability for a Bresse System with Hybrid Dissipation

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