Bresse System Research Articles

Attractors of a thermoelastic Bresse system with mass diffusion

AbstractThis 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.

Well-posedness and energy decay for Bresse system with microtemperatures effects in the presence of delay

Well-posedness and energy decay for Bresse system with microtemperatures effects in the presence of delay

Generalized approach for stability numbers of shear-damped Bresse systems with Cattaneo couplings

In this paper, by means of two general lemmas applicable to a wide variety of cases, we present a general formulation for the stability numbers associated with the thermoelastic Bresse system with heat flux given by Cattaneo's law and use it to show exponential stability of shear-damped versions of this system.

Energy decay of one-dimensional thermoelastic bresse system with distributed neutral delay and a second sound

Energy decay of one-dimensional thermoelastic bresse system with distributed neutral delay and a second sound

Asymptotic behavior for a semilinear Bresse system with variable coefficients and locally distributed nonlinear dissipation

In this paper, we consider a semilinear Bresse system in one dimensional bounded non homogeneous medium. We investigate stability issues for such a problem with a nonlinear damping acting in all three wave equations. We prove, firstly, the existence and uniqueness of the solutions by using the nonlinear semigroup method. Afterwords, we establish an uniform decay rates of the energy for these solutions without considering any restriction on the coefficients as well as the equality of the wave propagation speeds. Some techniques of the microlocal analysis theory are used in order to reach the desired asymptotics.

New stability result for bresse system with dual-phase-lag thermoelasticity

This work is devoted to the study of the time decay of the one-dimensional thermoelastic Bresse system where the dual-phase-lag heat conduction theory is used to model the heat transfer. In this theory, two relaxation parameters τ q and τ θ are proposed. By using the multplier method, we prove that the system is dissipative if 2 τ θ > τ q and exponentially stable by introducing a new stability number χ 1 . This result substantially improves earlier results in the literature.

Exploring Thermoelastic Effects in Damped Bresse Systems with Distributed Delay

In this work, we consider the one-dimensional thermoelastic Bresse system by addressing the aspects of nonlinear damping and distributed delay term acting on the first and the second equations. We prove a stability result without the common assumption regarding wave speeds under Neumann boundary conditions. We discover a new relationship between the decay rate of the solution and the growth of ϖ at infinity. Our results were achieved using the multiplier method and the perturbed modified energy, named Lyapunov functions together with some properties of convex functions.

Theoretical and numerical study of the decay in a viscoelastic Bresse System

Theoretical and numerical study of the decay in a viscoelastic Bresse System

Pointwise stabilization of Bresse systems

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Arched beams of Bresse type: New thermal couplings and pattern of stability

This is the second paper of a trilogy intended by the authors in what concerns a unified approach to the stability of thermoelastic arched beams of Bresse type under Fourier’s law. Differently of the first one, where the thermal couplings are regarded on the axial and bending displacements, here the thermal couplings are taken over the shear and bending forces. Such thermal effects still result in a new prototype of partially damped Bresse system whose stability results demand a proper approach. Combining a novel path of local estimates by means of the resolvent equation along with a control-observability analysis developed for elastic non-homogeneous systems of Bresse type proposed in trilogy’s first paper, we are able to provide a unified methodology of the asymptotic stability results, by proving the pattern of them with respect to boundary conditions and the action of temperature couplings, which is in compliance with our previous and present goal.

Exponential Stability for a Bresse System with Hybrid Dissipation

Exponential Stability for a Bresse System with Hybrid Dissipation

Decay rate of the solutions to the Cauchy problem of the Bresse system in thermoelasticity of type III with distributed delay

The decay rate of solutions to a Bresse system in thermoelasticity of type III with respect to the distributed delay term is the subject of this study. We demonstrate our major finding utilising the energy approach in the Fourier space.

Stabilization of Bresse system with thermodiffusion effects

Stabilization of Bresse system with thermodiffusion effects

Stability of a linear thermoelastic Bresse system with second sound under new conditions on the coefficients

AbstractIn this paper, we discuss the stability of a linear one‐dimensional thermoelastic Bresse system, where the coupling is given through the first component of the Bresse model with the heat conduction of second sound type. We state the well‐posedness and show the polynomial stability of the system, where the decay rate depends on the smoothness of initial data. Moreover, we prove the non exponential and the exponential decay depending on new conditions on the parameters of the system. The proof is based on a combination of the energy method and the frequency domain approach.

Stabilization of a Type III Thermoelastic Bresse System with Distributed Delay-time

Stabilization of a Type III Thermoelastic Bresse System with Distributed Delay-time

Upper semicontinuity of the global attractor for Bresse system with second sound

In this paper, we study the long-time dynamics of Bresse system under mixed homogeneous Dirichlet–Neumann boundary conditions. The heat conduction is given by Cattaneo's law. Only the shear angle displacement is damped via the dissipation from the Cattaneo's law, and the vertical displacement and the longitudinal displacement are free. Under quite general assumptions on the source term and based on the semigroup theory, we establish the global well-posedness and the existence of global attractors with finite fractal dimension in natural space energy. Finally, we prove the upper semicontinuous with respect to the relaxation time τ as it converges to zero.

Theoretical and computational decay results for a Bresse system with one infinite memory in the longitudinal displacement

<p style='text-indent:20px;'>In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory term acting in the third equation (longitudinal displacements). Under a general condition on the memory kernel (relaxation function), we establish a decay estimate of the energy of the system. Our decay result extends and improves some decay rates obtained in the literature such as the one in [<xref ref-type="bibr" rid="b27">27</xref>], [<xref ref-type="bibr" rid="b4">4</xref>], [<xref ref-type="bibr" rid="b33">33</xref>], [<xref ref-type="bibr" rid="b58">58</xref>] and [<xref ref-type="bibr" rid="b34">34</xref>]. The proof is based on the energy method together with convexity arguments. Numerical simulations are given to illustrate the theoretical decay result.</p>

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

<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>

New general decay results for a multi-dimensional Bresse system with viscoelastic boundary conditions

<p style='text-indent:20px;'>In this paper we consider a multi-dimensional Bresse with memory-type boundary conditions. By assuming minimal conditions on the resolvent kernel, we establish an optimal explicit and general energy decay result. This result is new and substantially improves earlier results in the literature.</p>

Internal exact-approximate controllability for the thermoelastic Bresse system

Internal exact-approximate controllability for the thermoelastic Bresse system