scholarly journals General Decay for the Degenerate Equation with a Memory Condition at the Boundary

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Su-Young Shin ◽  
Jum-Ran Kang
Keyword(s):  
Decay Rates ◽  
General Decay ◽  
Polynomial Decay ◽  
Degenerate Equation ◽  
Memory Condition ◽  
Relaxation Functions ◽  
Special Cases

We consider a degenerate equation with a memory condition at the boundary. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.

scholarly journals General decay of solutions of a thermoelastic Bresse system with viscoelastic boundary conditions

2021 ◽  
Vol 39 (6) ◽  
pp. 157-182
Author(s):  
Ammar Khemmoudj
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Decay Rates ◽  
General Decay ◽  
Polynomial Decay ◽  
Relaxation Functions ◽  
Bresse System ◽  
Decay Of Solutions ◽  
Special Cases

In this paper we consider a multidimensional thermoviscoelastic system of Bresse type where the heat conduction is given by Green and Naghdi theories. For a wider class of relaxation functions, We show that the dissipation produced by the memory eect is strong enough to produce a general decay results. We establish a general decay results, from which the usual exponential and polynomial decay rates are only special cases.

scholarly journals Boundary Stabilization of Memory Type for the Porous-Thermo-Elasticity System

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Abdelaziz Soufyane ◽  
Mounir Afilal ◽  
Mama Chacha
Keyword(s):  
Elastic System ◽  
Decay Rates ◽  
General Decay ◽  
Polynomial Decay ◽  
Boundary Stabilization ◽  
One Dimensional ◽  
Elasticity System ◽  
Special Cases ◽  
Memory Type ◽  
The One

We consider the one-dimensional viscoelastic Porous-Thermo-Elastic system. We establish a general decay results. The usual exponential and polynomial decay rates are only special cases.

scholarly journals General decay and blow-up for coupled Kirchhoff wave equations with dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mengxian Lv ◽  
Jianghao Hao
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Blow Up ◽  
Initial Energy ◽  
Decay Rates ◽  
General Decay ◽  
Dynamic Boundary Conditions ◽  
Positive Initial Energy ◽  
Relaxation Functions ◽  
Dynamic Boundary

<p style='text-indent:20px;'>In this paper we consider a system of viscoelastic wave equations of Kirchhoff type with dynamic boundary conditions. Supposing the relaxation functions <inline-formula><tex-math id="M1">\begin{document}$ g_i $\end{document}</tex-math></inline-formula> <inline-formula><tex-math id="M2">\begin{document}$ (i = 1, 2, \cdots, l) $\end{document}</tex-math></inline-formula> satisfy <inline-formula><tex-math id="M3">\begin{document}$ g_i(t)\leq-\xi_i(t)G(g_i(t)) $\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M4">\begin{document}$ G $\end{document}</tex-math></inline-formula> is an increasing and convex function near the origin and <inline-formula><tex-math id="M5">\begin{document}$ \xi_i $\end{document}</tex-math></inline-formula> are nonincreasing, we establish some optimal and general decay rates of the energy using the multiplier method and some properties of convex functions. Moreover, we obtain the finite time blow-up result of solution with nonpositive or arbitrary positive initial energy. The results in this paper are obtained without imposing any growth condition on weak damping term at the origin. Our results improve and generalize several earlier related results in the literature.</p>

scholarly journals Decay rates for solutions of a Timoshenko system with a memory condition at the boundary

2002 ◽  
Vol 7 (10) ◽  
pp. 531-546 ◽  
Author(s):  
Mauro de Lima Santos
Keyword(s):  
Asymptotic Behavior ◽  
Energy Decay ◽  
Decay Rates ◽  
Memory Condition ◽  
Timoshenko System ◽  
Relaxation Functions ◽  
Rate Of Decay ◽  
With Memory

We consider a Timoshenko system with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decay with the same rate of decay of the relaxation functions, that is, the energy decays exponentially when the relaxation functions decays exponentially and polynomially when the relaxation functions decays polynomially.

scholarly journals New general decay result for a system of two singular nonlocal viscoelastic equations with general source terms and a wide class of relaxation functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Adel M. Al-Mahdi ◽  
Salim A. Messaoudi
Keyword(s):  
Wide Class ◽  
Relaxation Function ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
General Assumption ◽  
General Decay ◽  
Source Terms ◽  
Relaxation Functions ◽  
Viscoelastic Equations ◽  
General Source

Abstract This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function $k_{i}$ k i , namely, $$\begin{aligned} k_{i}^{\prime }(t)\le -\xi _{i}(t) \Psi _{i} \bigl(k_{i}(t)\bigr),\quad i=1,2. \end{aligned}$$ k i ′ ( t ) ≤ − ξ i ( t ) Ψ i ( k i ( t ) ) , i = 1 , 2 . We establish a new general decay result that improves most of the existing results in the literature related to this system. Our result allows for a wider class of relaxation functions, from which we can recover the exponential and polynomial rates when $k_{i}(s) = s^{p}$ k i ( s ) = s p and p covers the full admissible range $[1, 2)$ [ 1 , 2 ) .

QCD corrections to heavy quark decays

2007 ◽  
Vol 85 (6) ◽  
pp. 613-617
Author(s):  
I Blokland
Keyword(s):  
Heavy Quark ◽  
Symbolic Computation ◽  
Decay Rates ◽  
Special Cases ◽  
Quark Decays ◽  
Quark Decay

The calculation of QCD corrections to heavy quark decay rates has progressed steadily in recent years. With the help of specialized techniques, symbolic computation, and a growing base of experience, a wide variety of special cases have been evaluated. These results have been applied to decays such as t → bW, b → s γ, b → u[Formula: see text]ν, and b → c[Formula: see text]ν. PACS Nos.: 12.38.Bx, 13.30.Ce

scholarly journals General decay rate of a weakly dissipative viscoelastic equation with a general damping

2020 ◽  
Vol 40 (6) ◽  
pp. 647-666
Author(s):  
Khaleel Anaya ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Wide Class ◽  
Nonlinear Damping ◽  
Numerical Results ◽  
General Decay ◽  
General Decay Rate ◽  
Relaxation Functions ◽  
Viscoelastic Equation

In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.

scholarly journals General Decay Rates for a Laminated Beam with Memory

2019 ◽  
Vol 23 (5) ◽  
pp. 1227-1252 ◽  
Author(s):  
Zhijing Chen ◽  
Wenjun Liu ◽  
Dongqin Chen
Keyword(s):  
Decay Rates ◽  
General Decay ◽  
Laminated Beam ◽  
With Memory

General decay in a Timoshenko-type system with thermoelasticity with second sound

2015 ◽  
Vol 4 (4) ◽  
pp. 263-284 ◽  
Author(s):  
Mohamed Ali Ayadi ◽  
Ahmed Bchatnia ◽  
Makram Hamouda ◽  
Salim Messaoudi
Keyword(s):  
Group Theory ◽  
Type System ◽  
General Decay ◽  
Regularity Of Solutions ◽  
Well Posedness ◽  
Second Sound ◽  
Semi Group ◽  
Stability Number ◽  
Timoshenko System ◽  
Relaxation Functions

AbstractIn this article, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We discuss the well-posedness and the regularity of solutions using the semi-group theory. Moreover, we establish an explicit and general decay result for a wide class of relaxation functions, which depend on a stability number μ.

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