Bresse System Research Articles

Bresse system with Fourier law on shear force

Our goal in this paper is to investigate the effect of Fourier law on a new coupling for the Bresse system. We give an explicit characterization on the decay rate that can be exponential or polynomial type, depending on the relation between the coefficients of the wave speed propagation.

The lack of exponential stability of the hybrid Bresse system

In this paper we consider the dissipative Bresse system with an attached hollow-tip body that contains granular material, the resulting model being called hybrid system. Our main result is to show that the corresponding model is not exponentially stable. Moreover, we show that the solution decays polynomially to zero as (1+t)−1/2 when t→∞.

The Cauchy problem of the Bresse system in thermoelasticity of type III

In this paper, we consider the Bresse system coupled with the Green and Naghdi type-III theory of heat conduction. We prove that the decay rate of the solution is very slow. In fact, we show that the -norm of the solution decays with the rate of similar to the one obtained for the Timoshenko system in thermoelasticity of type III. Furthermore, we found that the wave speeds of the equations control the decay rate of the solution with respect to the regularity of the initial data. In addition, we prove that the solution enjoys the property of regularity loss.

Global existence and energy decay of solutions to a Bresse system with delay terms

We consider the Bresse system in bounded domain with delay terms in the internal feedbacks and prove the global existence of its solutions in Sobolev spaces by means of semigroup theory under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method.

Exact controllability for Bresse system with variable coefficients

This paper is concerned with the internal exact controllability of a generalized Bresse system with variable coefficients, which the controls functions acts in an arbitrarily small subinterval (l1,l2) of (0,L). Our computation suggests a minimal time control and a region where the controls are more effective. The variable coefficients can be viewed as a generalization of Laplacian operator. The main result is obtained by applying Hilbert Uniqueness Method proposed by Lions, without using the Holmgren's uniqueness theorem or the hypothesis of equal‐speed waves of propagation. Copyright © 2015 John Wiley & Sons, Ltd.

Asymptotic stability of thermoelastic systems of Bresse type

We provide a comprehensive stability analysis of the thermoelastic Bresse system (also known as the circular arch problem). In particular, assuming a temperature evolution of Gurtin–Pipkin type, we establish a necessary and sufficient condition for exponential stability in terms of the structural parameters of the problem. As a byproduct, a complete characterization of the longtime behavior of Bresse-type systems with Fourier, Maxwell–Cattaneo and Coleman–Gurtin thermal laws is obtained. Our main theorem also subsumes some recent achievements in the stability properties of thermoelastic Timoshenko systems with classical and nonclassical heat conduction.

The Bresse system in thermoelasticity

In this paper, we consider the Bresse system coupled with the Fourier law of heat conduction. We prove that the decay rate of the solution is very slow. In fact, we show that the L2‐norm of the solution decays with the rate of (1 + t)−1/12 similar to the one obtained for the Timoshenko system. In addition, we found that the wave speed of the first two equations still control the decay rate of the solution with respect to the regularity of the initial data. This seems to be the first result dealing with the behavior of the Cauchy problem in the Bresse–Fourier model. Copyright © 2014 John Wiley & Sons, Ltd.

Asymptotic behavior to Bresse system with past history

In this paper we consider the Bresse system with past history acting in the shear angle displacement. We show the exponential decay of the solution if and only if the wave speeds are the same. On the contrary, we show that the Bresse system is polynomial stable with optimal decay rate. The systems of equations considered here introduce new mathematical difficulties in order to determine the asymptotic behavior. As far as the authors know, there have been no contributions made in this sense.

Bresse system with infinite memories

In this paper, we consider a one-dimensional linear Bresse system with infinite memories acting in the three equations of the system. We establish well-posedness and asymptotic stability results for the system under some conditions imposed into the relaxation functions regardless to the speeds of wave propagations. Copyright © 2014 John Wiley & Sons, Ltd.

Stability and optimality of decay rate for a weakly dissipative Bresse system

AbstractThis paper is concerned with asymptotic stability of a Bresse system with two frictional dissipations. Under mathematical condition of equal speed of wave propagation, we prove that the system is exponentially stable. Otherwise, we show that Bresse system is not exponentially stable. Then, in the latter case, by using a recent result in linear operator theory, we prove the solution decays polynomially to zero with optimal decay rate. Better rates of polynomial decay depending on the regularity of initial data are also achieved. Copyright © 2014 John Wiley & Sons, Ltd.

Stability criterion to explicit finite difference applied to the Bresse system

In this work, we show that the stability criterion of the explicit time integration method applied to the Bresse system is given by $$\begin{aligned} \Delta t\le \displaystyle \frac{2\epsilon }{\sqrt{ \bigg (12 +\displaystyle \frac{\epsilon ^2}{R^2}\bigg )}\displaystyle \frac{k G}{\rho }}, \end{aligned}$$ where the thickness \(\epsilon \) constitutes a limitation to compute the numerical solutions. This restriction to the stability criterion is not standard (is not CFL condition) and if \(\epsilon <<1\) it is very restrictive to numerical computations. To overcome this restriction, we use the technics performed by Wright [Commun Appl Numer Methods 3:181–185 (1987), Commun Numer Methods Eng 14:81–86 (1998)] to minimize the influence of \(\epsilon \) on stability criterion such that the CFL condition prevails.

Global existence of solutions for the thermoelastic Bresse system

In this paper, using the semigroup approach, we obtain the global existence of solutions for linear (nonlinear) homogeneous (nonhomogeneous) thermoelastic Bresse System.

Global existence of solutions for the thermoelastic Bresse system

Global existence of solutions for the thermoelastic Bresse system

Energy Decay Rate for Bresse System with Nonlinear Localized Damping

Energy Decay Rate for Bresse System with Nonlinear Localized Damping

The effect of the wave speeds and the frictional damping terms on the decay rate of the Bresse system

In this paper, we consider the Bresse system with frictional damping terms. We investigated the relationship between the frictional damping terms, the wave speeds of propagation and their influence on the decay rate of the solution. We proved that in many cases the solution enjoys the decay property of regularity-loss type. We introduced a new assumption on the wave speeds that controls the behavior of the solution of the Bresse system. In addition, when the coefficient $l $ goes to zero, we showed that the solution of the Bresse system decays faster than the one of the Timoshenko system. This result seems to be the first one to give the decay rate of the solution of the Bresse system in unbounded domain.

Spectral analysis and stability of thermoelastic Bresse system with second sound and boundary viscoelastic damping

AbstractIn this paper, we consider the energy decay rate of a thermoelastic Bresse system with variable coefficients. Assume that the thermo‐propagation in the system satisfies the Cattaneo's law, which can eliminate the paradox of infinite speed of thermal propagation in the assumption of the Fourier's law in the classical theory of thermoelasticity. Meanwhile, we also discuss the effect of a boundary viscoelastic damping on the stability of this system. By a detailed spectral analysis, we obtain the expressions of the spectrum and deduce some spectral properties of the system. Then based on the distribution of the spectrum, we prove that the energy of the system with a boundary viscoelastic damping decays exponentially. However, it no longer decays exponentially if there is no boundary damping. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Asymptotic stability for Bresse systems

In this paper consider a vibrating system of Bresse type in a one-dimensional bounded domain with a nonlinear damping acting in the equation of the shear angle displacement, and nonlinear localized damping in other equations. We show the asymptotic stability without imposing conditions about the equal-speed wave propagation, using a method developed by Lasiecka and Tataru [9].

Decay rates for Bresse system with arbitrary nonlinear localized damping

In this paper we consider a vibrating system of Bresse type, in a one-dimensional bounded domain with nonlinear localized damping mechanisms acting in all the three wave equations. We obtain some rates of decay for its solutions with no restrictions around the coefficients as well as the condition of equal-speed wave propagation. A new result concerning an internal observability for the conservative system was also proved in order to reach the asymptotics above.

Stabilisation faible interne locale de système élastique de Bresse

In [1], Alabau-Boussouira et al. (2011) studied the exponential and polynomial stability of the Bresse system with one globally distributed dissipation law. In this Note, our goal is to extend the results from Alabau-Boussouira et al. (2011) [1], by taking into consideration the important case when the dissipation law is locally distributed and to improve the polynomial energy decay rate. We then study the energy decay rate of the Bresse system with one locally internal distributed dissipation law acting on the equation about the shear angle displacement. Under the equal speed wave propagation condition, we show that the system is exponentially stable. On the contrary, we establish a new polynomial energy decay rate.

Stability and global attractors for thermoelastic Bresse system

The Editor and Publishers Taylor & Francis are retracting the above article from publication in Applicable Analysis. This paper was previously published in online only form as part of Taylor & Fran...