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 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 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 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 of solutions of a Bresse system with viscoelastic boundary conditions

2017 ◽  
Vol 37 (9) ◽  
pp. 4857-4876 ◽  
Author(s):  
Ammar Khemmoudj ◽  
◽  
Taklit Hamadouche
Keyword(s):  
Boundary Conditions ◽  
General Decay ◽  
Bresse System ◽  
Decay Of Solutions

scholarly journals INTEGRAL TRANSFORMATION IN A PARTIALLY BOUNDED REGION WITH A RADIAL THERMAL FLOW

2018 ◽  
Vol 13 (6) ◽  
pp. 89-96
Author(s):  
E. M. Kartashov
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Green's Functions ◽  
Green’S Functions ◽  
Integral Transformation ◽  
Bounded Region ◽  
Integral Transformations ◽  
Functional Relations ◽  
Special Cases ◽  
Unsteady Heat Conduction

A mathematical theory is developed for constructing integral transformations in a partially bounded region with a radial heat flow - a massive body bounded from the inside by a cylindrical cavity. Constructed: an integral transformation, the image of the operator on the right side of the equation of unsteady heat conduction, the inversion formula for the image of the desired function. The proposed approach favorably differs from the classical theory of differential equations of mathematical physics for the construction of generalized integral transformations based on the eigenfunctions of the corresponding singular Sturm-Liouville problems. The developed method is based on the operational solution of the initial boundary problems of unsteady heat conduction with an initial function of a general form L2(r0,∞) belonging to the r > r0 region and homogeneous boundary conditions and is associated with the calculation of the Riemann-Mellin contour integrals from images containing various combinations of modified Bessel functions. At the same time, for the above-mentioned region, the method of Green's functions was developed by constructing integral representations of analytical solutions of the first, second and third boundary value problems through inhomogeneities in the initial formulation of the problem (boundary conditions, source function in the initial equation). Mathematical models for finding the corresponding Green's functions are formulated, and functional relations of all three Green functions included in the presented integral formula are written out with the help of the developed theory of integral transformations. The functional relations constructed in the article can be used when considering numerous special cases of practical thermal physics. The specific possible applications of the presented results in many areas of science and technology are given.

HEAT CONDUCTION IN DIELECTRIC ATOMIC CHAINS WITH ON-SITE POTENTIAL

2010 ◽  
Vol 24 (06) ◽  
pp. 521-526 ◽  
Author(s):  
JIN-XING LI ◽  
FEI LIU ◽  
TAO CHEN
Keyword(s):  
Numerical Simulation ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Coupling Strength ◽  
Thermal Transport ◽  
Different Boundary Conditions ◽  
Strength Coefficient ◽  
Special Cases ◽  
Atomic Chains

Heat conduction in dielectric atomic chains with on-site potential were studied by means of FKM formalism. Using numerical simulation we found that the on-site potential plays an important role in quantum thermal transport. As special cases, the "Fourier-like behavior" J ∝ 1/N was obtained also for different boundary conditions. The influence of boundaries can be regulated by the coupling strength coefficient of the on-site potential.

scholarly journals Global Existence and General Decay of Solutions for a Quasilinear System with Degenerate Damping Terms

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Fatma Ekinci ◽  
Erhan Pișkin ◽  
Salah Mahmoud Boulaaras ◽  
Ibrahim Mekawy
Keyword(s):  
Boundary Condition ◽  
Global Existence ◽  
Recent Work ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
General Decay ◽  
Quasilinear System ◽  
Relaxation Functions ◽  
Decay Of Solutions ◽  
Viscoelastic Equations

In this work, we consider a quasilinear system of viscoelastic equations with degenerate damping, dispersion, and source terms under Dirichlet boundary condition. Under some restrictions on the initial datum and standard conditions on relaxation functions, we study global existence and general decay of solutions. The results obtained here are generalization of the previous recent work.

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