scholarly journals On the asymptotic behavior of solutions of anisotropic viscoelastic body

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yassine Letoufa ◽  
Hamid Benseridi ◽  
Salah Boulaaras ◽  
Mourad Dilmi
Keyword(s):  
Asymptotic Behavior ◽  
Three Dimensional ◽  
Viscoelastic Body ◽  
Weak Form ◽  
Uniqueness Result ◽  
Limit Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Quasistatic Problem ◽  
Rigid Plane ◽  
Tresca’S Friction

AbstractThe quasistatic problem of a viscoelastic body in a three-dimensional thin domain with Tresca’s friction law is considered. The viscoelasticity coefficients and data for this system are assumed to vary with respect to the thickness ε. The asymptotic behavior of weak solution, when ε tends to zero, is proved, and the limit solution is identified in a new data system. We show that when the thin layer disappears, its traces form a new contact law between the rigid plane and the viscoelastic body. In which case, a generalized weak form equation is formulated, the uniqueness result for the limit problem is also proved.

scholarly journals On the Asymptotic Behavior of D-Solutions to the Displacement Problem of Linear Elastostatics in Exterior Domains

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 77
Author(s):  
Vincenzo Coscia
Keyword(s):  
Asymptotic Behavior ◽  
Lipschitz Domain ◽  
Three Dimensional ◽  
Finite Energy ◽  
Asymptotic Behavior Of Solutions ◽  
Exterior Domains ◽  
Displacement Problem ◽  
Linear Elastostatics

We study the asymptotic behavior of solutions with finite energy to the displacement problem of linear elastostatics in a three-dimensional exterior Lipschitz domain.

ASYMPTOTICS OF A SPECTRAL PROBLEM ASSOCIATED WITH THE NEUMANN SIEVE

2005 ◽  
Vol 03 (01) ◽  
pp. 69-87 ◽  
Author(s):  
DANIEL ONOFREI ◽  
BOGDAN VERNESCU
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Spectral Problem ◽  
Three Dimensional ◽  
Simple Eigenvalue ◽  
Limit Problem ◽  
Two Dimensional ◽  
Entire Sequence

In this paper, we analyze the asymptotic behavior of a Stekloff spectral problem associated with the Neumann Sieve model, i.e. a three-dimensional set Ω, cut by a hyperplane Σ where each of the two-dimensional holes, ∊-periodically distributed on Σ, have diameter r∊. Depending on the asymptotic behavior of the ratios [Formula: see text] we find the limit problem of the ∊ spectral problem and prove that the sequences [Formula: see text], formed by the nth eigenvalue of the ∊ problem, converge to λn, the nth eigenvalue of the limit problem, for any n ∈ N. We also prove the weak convergence, on a subsequence, of the associated sequence of eigenvectors [Formula: see text], to an eigenvector associated with λn. When λn is a simple eigenvalue, we show that the entire sequence of the eigenvectors converges. As a consequence, similar results hold for the spectrum of the DtN map associated to this model.

scholarly journals A Study of the Anisotropic Static Elasticity System in Thin Domain

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yassine Letoufa ◽  
Salah Mahmoud Boulaaras ◽  
Hamid Benseridi ◽  
Mourad Dilmi ◽  
Asma Alharbi
Keyword(s):  
Weak Form ◽  
Equation Model ◽  
Limit Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Mathematical Framework ◽  
Thin Domain ◽  
Elasticity System ◽  
Static Elasticity ◽  
Linearized Elasticity ◽  
Linearized Elasticity System

We study the asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin domain of ℝ 3 which has a fixed cross-section in the ℝ 2 plane with Tresca friction condition. The novelty here is that stress tensor has given by the most general form of Hooke’s law for anisotropic materials. We prove the convergence theorems for the transition 3D-2D when one dimension of the domain tends to zero. The necessary mathematical framework and (2D) equation model with a specific weak form of the Reynolds equation are determined. Finally, the properties of solution of the limit problem are given, in which it is confirmed that the limit problem is well defined.

scholarly journals On a solvable three-dimensional system of difference equations

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1167-1186
Author(s):  
Merve Kara ◽  
Yasin Yazlik
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Three Dimensional ◽  
Asymptotic Behavior Of Solutions ◽  
Dimensional System ◽  
Real Numbers ◽  
System Of Difference Equations ◽  
Initial Values ◽  
Forbidden Set ◽  
Three Dimensional System

In this paper, we show that the following three-dimensional system of difference equations xn = zn-2xn-3/axn-3 + byn-1, yn = xn-2yn-3/cyn-3 + dzn-1, zn = yn-2zn-3/ezn-3+ fxn-1, n ? N0, where the parameters a, b, c, d, e, f and the initial values x-i, y-i, z-i, i ? {1, 2, 3}, are real numbers, can be solved, extending further some results in literature. Also, we determine the asymptotic behavior of solutions and the forbidden set of the initial values by using the obtained formulas.

scholarly journals Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Abdelkader Saadallah ◽  
Nadhir Chougui ◽  
Fares Yazid ◽  
Mohamed Abdalla ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Reynolds Equation ◽  
Limit Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Thin Domain

In this paper, we study the asymptotic behavior of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. We study the limit when the ε tends to zero, we prove the convergence of the unknowns which are the velocity and the pressure of the fluid, and we obtain the limit problem and the specific Reynolds equation.

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