scholarly journals Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation

2017 ◽  
Vol 35 (3) ◽  
pp. 203 ◽  
Author(s):  
Aissa Guesmia
Keyword(s):  
Decay Rate ◽  
Bounded Domain ◽  
Decay Rates ◽  
Kirchhoff Equation ◽  
Well Posedness ◽  
Kirchhoff Type ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
Optimal Decay Rate ◽  
Finite Memory

In this paper, we investigate the well-posedness as well as optimal decay rate estimates of the energy associated with a Kirchhoff-Carrier problem in n-dimensional bounded domain under an internal finite memory. The considered class of memory kernels is very wide and allows us to derive new and optimal decay rate estimates then those ones considered previously in the literature for Kirchhoff-type models.

scholarly journals Optimal Decay Rates for Kirchhoff Plates with Intermediate Damping

2020 ◽  
Vol 21 (2) ◽  
pp. 261
Author(s):  
J. C. V. Bravo ◽  
H. P. Oquendo ◽  
J. E. M. Rivera
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Decay Rates ◽  
Kirchhoff Plates ◽  
Optimal Decay Rates ◽  
Optimal Decay

In this paper we study the asymptotic behavior of Kirchhoff plates with intermediate damping. The damping considered contemplates the frictional and the Kelvin-Voigt type dampings. We show that the semigroup those equations decays polynomially in time at least with the rate t^{-1/(2-2θ)}, where θ is a parameter in the interval [0,1[. Moreover, we prove that this decay rate is optimal.

Global well-posedness and decay estimates for three-dimensional compressible Navier–Stokes–Allen–Cahn systems

2021 ◽  
pp. 1-32
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Three Dimensional ◽  
Decay Rates ◽  
Navier Stokes ◽  
Small Data ◽  
Well Posedness ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
The Cauchy Problem ◽  
Time Decay Rates ◽  
Derivatives Of

We study the small data global well-posedness and time-decay rates of solutions to the Cauchy problem for three-dimensional compressible Navier–Stokes–Allen–Cahn equations via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, the $\dot {H}^{-s}$ ( $0\leq s<\frac {3}{2}$ ) negative Sobolev norms is shown to be preserved along time evolution and enhance the decay rates.

scholarly journals On global well-posedness and decay of 3D Ericksen-Leslie system

2021 ◽  
Vol 6 (11) ◽  
pp. 12660-12679
Author(s):  
Xiufang Zhao ◽  
◽  
Ning Duan ◽  
Keyword(s):  
Strong Solutions ◽  
Decay Rates ◽  
Well Posedness ◽  
Small Initial Data ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
Liquid Crystal System ◽  
The Cauchy Problem ◽  
Derivatives Of ◽  
Leslie System

<abstract><p>In this paper, the small initial data global well-posedness and time decay estimates of strong solutions to the Cauchy problem of 3D incompressible liquid crystal system with general Leslie stress tensor are studied. First, assuming that $ \|u_0\|_{\dot{H}^{\frac12+\varepsilon}}+\|d_0-d_*\|_{\dot{H}^{\frac32+\varepsilon}} $ ($ \varepsilon &gt; 0) $ is sufficiently small, we obtain the global well-posedness of strong solutions. Moreover, the $ L^p $–$ L^2 $ ($ \frac32\leq p\leq2 $) type optimal decay rates of the higher-order spatial derivatives of solutions are also obtained. The $ \dot{H}^{-s} $ ($ 0\leq s &lt; \frac12 $) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.</p></abstract>

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.

On the global polynomial stabilization and observation with optimal decay rate

2021 ◽  
Vol 153 ◽  
pp. 111447
Author(s):  
Chaker Jammazi ◽  
Mohamed Boutayeb ◽  
Ghada Bouamaied
Keyword(s):  
Decay Rate ◽  
Optimal Decay ◽  
Optimal Decay Rate ◽  
Polynomial Stabilization
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