On the Asymptotic Behavior of an Interface Problem in a Thin Domain

Benseridi, Hamid; Letoufa, Yassine; Dilmi, Mourad

doi:10.1007/s40010-019-00598-4

Cited by 6 publications

(11 citation statements)

References 10 publications

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“…To prove (59), we use those similar steps as in [2,5,[9][10][11], by integrating (46) from 0 to z, and taking into account A i3j3 depending only on x, we obtain…”

Section: Limit Problem and Main Resultsmentioning

confidence: 99%

“…Let us mention for example [1][2][3][4][5][6][7][8] in which the authors worked on the asymptotic behavior for the linearized elasticity system with different boundary conditions. Some problems of Newtonian or non-Newtonian fluids are considered in [9][10][11] where the authors proved a limit problem that gives a distribution of velocity and pressure through the weak form of the Reynolds equation. In [6,7], the authors demonstrate the transition 3D-1D in anisotropic heterogeneous linearized elasticity; so, we mention here that this phenomenon has been studied only about strong solutions, without friction law.…”

Section: Introductionmentioning

confidence: 99%

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A Study of the Anisotropic Static Elasticity System in Thin Domain

Letoufa

Boulaaras

Benseridi

et al. 2021

Journal of Function Spaces

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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.

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“…To prove (59), we use those similar steps as in [2,5,[9][10][11], by integrating (46) from 0 to z, and taking into account A i3j3 depending only on x, we obtain…”

Section: Limit Problem and Main Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Study of the Anisotropic Static Elasticity System in Thin Domain

Letoufa

Boulaaras

Benseridi

et al. 2021

Journal of Function Spaces

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“…Moreover, this law and its traces meet the basic equation of motion in (4.2)-(4.3) and the boundary conditions of the Tresca friction in (4.10)-(4.11). The phenomenon is described mathematically by the weak formula (4.12), known as the Reynolds equation, and has been proved in many papers for the particular cases, see [1,2,4,7,12]. Specifically, if A ε = 0, the model matches the case of the anisotropic linearized elasticity system and has been studied in [13,14].…”

Section: Discussionmentioning

confidence: 99%

“…Simulation and asymptotic behavior have been performed for many physical milieu that occupy thin layers of R 3 in a lot of mechanical and mathematical papers in [1,8,9,12], both for Newtonian and non-Newtonian fluids, including visco-plastic materials. Otherwise, the materials related to the linear theory of elasticity have been studied in research papers conducted by Benseridi et al in [4][5][6]16] and others in [2,14,16].…”

Section: Introductionmentioning

confidence: 99%

On the asymptotic behavior of solutions of anisotropic viscoelastic body

et al. 2021

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The 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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“…This work gives an extension to describe the flow of fluids in a dynamic system to some of the results obtained in a series of papers [1,2,4,5,9], in which the authors considered a stationary case only of the general equations describing the motion of some fluid flows in bounded thin domain, with slip and mixed boundary conditions. The aim of this paper is to study the asymptotic analysis of an incompressible Bingham fluid in a dynamic regime in a three dimensional thin domain mixed boundary and subject to slip phenomenon on a part of the boundary.…”

Section: Introductionmentioning

confidence: 99%