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.

ON THE MAXIMUM MODULUS THEOREM IN LINEAR ELASTOSTATICS FOR EXTERIOR DOMAINS

1996 ◽  
Vol 06 (06) ◽  
pp. 721-728
Author(s):  
GIULIO STARITA
Keyword(s):  
Positive Constant ◽  
Three Dimensional ◽  
Maximum Modulus ◽  
Finite Energy ◽  
Exterior Domains ◽  
Dirichlet Data ◽  
Maximum Value ◽  
Linear Elastostatics ◽  
Maximum Modulus Theorem

This paper deals with the system of linear elastostatics in exterior three-dimensional domains. We prove that the modulus of every solution with finite energy of such a system may be majorized by a positive constant times the maximum value of the modulus of the Dirichlet data at the boundary (maximum modulus theorem).

scholarly journals A Note on the Displacement Problem of Elastostatics with Singular Boundary Values

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 46 ◽  
Author(s):  
Alfonsina Tartaglione
Keyword(s):  
Elastic Body ◽  
Function Class ◽  
Singular Boundary ◽  
Regular Boundary ◽  
Boundary Values ◽  
Exterior Domains ◽  
Displacement Problem ◽  
Natural Function ◽  
Linear Elastostatics ◽  
Class C

The displacement problem of linear elastostatics in bounded and exterior domains with a non-regular boundary datum a is considered. Precisely, if the elastic body is represented by a domain of class C k ( k ≥ 2 ) of R 3 and a ∈ W 2 − k − 1 / q , q ( ∂ Ω ) , q ∈ ( 1 , + ∞ ) , then it is proved that there exists a solution which is of class C ∞ in the interior and takes the boundary value in a well-defined sense. Moreover, it is unique in a natural function class.

scholarly journals Mixed Boundary Value Problems for the Elasticity System in Exterior Domains

2019 ◽  
Vol 24 (2) ◽  
pp. 58
Author(s):  
Hovik A. Matevossian
Keyword(s):  
Asymptotic Behavior ◽  
Variational Principle ◽  
Mixed Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Compact Set ◽  
Uniqueness Theorems ◽  
Energy Integral ◽  
Exterior Domains ◽  
Mixed Problems ◽  
Elasticity System

We study the properties of solutions of the mixed Dirichlet–Robin and Neumann–Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy integral with weight | x | a is finite for such solutions. We use the variational principle and depending on the value of the parameter a, obtain uniqueness (non-uniqueness) theorems of the mixed problems or present exact formulas for the dimension of the space of solutions.

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 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.

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