scholarly journals New stability result for a Bresse system with one infinite memory in the shear angle equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Saeed M. Ali
Keyword(s):  
Asymptotic Stability ◽  
Initial Data ◽  
General Condition ◽  
Relaxation Function ◽  
Stability Result ◽  
Shear Angle ◽  
Boundedness Condition ◽  
Infinite Memory ◽  
One Dimensional ◽  
Bresse System

<p style='text-indent:20px;'>In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory acting in the second equation (the shear angle equation) of the system. We prove that the asymptotic stability of the system holds under some general condition imposed into the relaxation function, precisely,</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ g^{\prime}(t)\le -\xi(t) G(g(t)). $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>The proof is based on the multiplier method and makes use of convex functions and some inequalities. More specifically, we remove the constraint imposed on the boundedness condition on the initial data <inline-formula><tex-math id="M1">\begin{document}$ \eta{0x} $\end{document}</tex-math></inline-formula>. This study generalizes and improves previous literature outcomes.</p>

scholarly journals A New Result of Stability for Thermoelastic-Bresse System of Second Sound Related with Forcing, Delay, and Past History Terms

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Djamel Ouchenane ◽  
Zineb Khalili ◽  
Fares Yazid ◽  
Mohamed Abdalla ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Asymptotic Stability ◽  
Past History ◽  
Stability Result ◽  
Shear Angle ◽  
Well Posedness ◽  
Second Sound ◽  
One Dimensional ◽  
Delay Term ◽  
Bresse System ◽  
Semigroup Method

We consider a one-dimensional linear thermoelastic Bresse system with delay term, forcing, and infinity history acting on the shear angle displacement. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method, where an asymptotic stability result of global solution is obtained.

scholarly journals Uniform and weak stability of Bresse system with one infinite memory in the shear angle displacements

2021 ◽  
Author(s):  
Rania Bekhouche ◽  
Aissa Guesmia ◽  
Salim Messaoudi
Keyword(s):  
Semigroup Theory ◽  
Open Interval ◽  
Weak Decay ◽  
Shear Angle ◽  
Well Posedness ◽  
Decay Estimates ◽  
Weak Stability ◽  
Infinite Memory ◽  
One Dimensional ◽  
Bresse System

AbstractIn this paper, we consider a one-dimensional linear Bresse system in a bounded open interval with one infinite memory acting only on the shear angle equation. First, we establish the well posedness using the semigroup theory. Then, we prove two general (uniform and weak) decay estimates depending on the speeds of wave propagations and the arbitrary growth at infinity of the relaxation function.

Asymptotic stability for a laminated beam with structural damping and infinite memory

2020 ◽  
Vol 25 (10) ◽  
pp. 1979-2004 ◽  
Author(s):  
Wenjun Liu ◽  
Xiangyu Kong ◽  
Gang Li
Keyword(s):  
Wave Propagation ◽  
Relaxation Function ◽  
Rotation Angle ◽  
Structural Damping ◽  
Laminated Beam ◽  
Infinite Memory ◽  
One Dimensional ◽  
Special Cases ◽  
Lack Of Exponential Stability ◽  
Well Posed

In this paper, we consider a one-dimensional laminated beam with structural damping and an infinite memory acting on the effective rotation angle. Under appropriate assumptions imposed on the relaxation function, we show that the system is well-posed by using the Hille–Yosida theorem, and then we establish general decay results, from which exponential and polynomial decays are only special cases, in the case of equal speeds of wave propagation as well as that of nonequal speeds. In the particular case when the wave propagation speeds are different and the relaxation function decays exponentially, we show the lack of exponential stability.

scholarly journals A new stability result for a thermoelastic Bresse system with viscoelastic damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Soh Edwin Mukiawa ◽  
Cyril Dennis Enyi ◽  
Tijani Abdulaziz Apalara
Keyword(s):  
Stability Result ◽  
Bending Moment ◽  
Decay Rates ◽  
Viscoelastic Damping ◽  
Physical Parameters ◽  
Bresse System ◽  
Solution Energy ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
Weaker Conditions

AbstractWe investigate a thermoelastic Bresse system with viscoelastic damping acting on the shear force and heat conduction acting on the bending moment. We show that with weaker conditions on the relaxation function and physical parameters, the solution energy has general and optimal decay rates. Some examples are given to illustrate the findings.

PACKING SUBORDINACY WITH APPLICATION TO SPECTRAL CONTINUITY

2019 ◽  
Vol 108 (2) ◽  
pp. 226-244 ◽  
Author(s):  
V. R. BAZAO ◽  
S. L. CARVALHO ◽  
C. R. DE OLIVEIRA
Keyword(s):  
Continuous Spectrum ◽  
Dimensional Stability ◽  
Schrödinger Operators ◽  
Stability Result ◽  
Schrodinger Operators ◽  
Spectral Measures ◽  
One Dimensional ◽  
Continuity Properties ◽  
Rotation Numbers ◽  
Spectral Continuity

By using methods of subordinacy theory, we study packing continuity properties of spectral measures of discrete one-dimensional Schrödinger operators acting on the whole line. Then we apply these methods to Sturmian operators with rotation numbers of quasibounded density to show that they have purely $\unicode[STIX]{x1D6FC}$-packing continuous spectrum. A dimensional stability result is also mentioned.

Stability of planar rarefaction wave to the 3D bipolar Vlasov–Poisson–Boltzmann system

2019 ◽  
Vol 30 (01) ◽  
pp. 23-104 ◽  
Author(s):  
Shu Wang ◽  
Teng Wang
Keyword(s):  
Wave Propagation ◽  
Boltzmann Equation ◽  
Asymptotic Stability ◽  
Rarefaction Wave ◽  
Stability Result ◽  
Three Dimensions ◽  
Wave Patterns ◽  
Shock Profiles ◽  
Poisson Boltzmann ◽  
Math Phys

We investigate the time-asymptotic stability of planar rarefaction wave for the 3D bipolar Vlasov–Poisson Boltzmann (VPB) system, based on the micro–macro decompositions introduced in [T. P. Liu and S. H. Yu, Boltzmann equation: Micro–macro decompositions and positivity of shock profiles, Comm. Math. Phys. 246 (2004) 133–179; Energy method for the Boltzmann equation, Physica D 188 (2004) 178–192] and our new observations on the underlying wave structures of the equation to overcome the difficulties due to the wave propagation along the transverse directions and its interactions with the planar rarefaction wave. Note that this is the first stability result of basic wave patterns for bipolar VPB system in three dimensions.

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