Asymptotic analysis for the elasticity system with Tresca and maximal monotone graph conditions
Volume 29, Issue 3, pp 252--263
https://doi.org/10.22436/jmcs.029.03.04
Publication Date: October 21, 2022
Submission Date: February 10, 2022
Revision Date: May 11, 2022
Accteptance Date: July 29, 2022
Authors
M. Boudersa
- Departement of mathematics, Unversity of Batna 2, Algeria.
H. Benseridi
- Departement of mathematics, Unversity of Setif 1, Algeria.
Abstract
In this paper, we consider the stationary problem in three dimensional thin domain \(\Omega ^{\varepsilon }\) with maximal monotone graph and Tresca conditions. In the first step, we present the problem statement and give the variational formulation. We then study the asymptotic behavior when one dimension of the domain tends to zero. In the latter case a specific Reynolds limit equation is obtained and the uniqueness of the displacement of the limit problem are proved.
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ISRP Style
M. Boudersa, H. Benseridi, Asymptotic analysis for the elasticity system with Tresca and maximal monotone graph conditions, Journal of Mathematics and Computer Science, 29 (2023), no. 3, 252--263
AMA Style
Boudersa M., Benseridi H., Asymptotic analysis for the elasticity system with Tresca and maximal monotone graph conditions. J Math Comput SCI-JM. (2023); 29(3):252--263
Chicago/Turabian Style
Boudersa, M., Benseridi, H.. "Asymptotic analysis for the elasticity system with Tresca and maximal monotone graph conditions." Journal of Mathematics and Computer Science, 29, no. 3 (2023): 252--263
Keywords
- Asymptotic approach
- maximal monotone graph
- Tresca law
- variational problem
- weak solution
MSC
References
-
[1]
G. Bayada, M. Boukrouche, On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions, J. Math. Anal. Appl., 282 (2003), 212--231
-
[2]
H. Benseridi, M. Dilmi, Some inequalities and asymptotic behaviour of dynamic problem of linear elasticity, Georgian Math. J., 20 (2013), 25--41
-
[3]
H. Benseridi, M. Dilmi, A. Saadallah, Asymptotic behaviour of a nonlinear boundary value problem with friction, Proc. Nat. Acad. Sci. India Sect. A, 88 (2018), 55--63
-
[4]
D. Benterki, H. Benseridi, M. Dilmi, Asymptotic study of a boundary value problem governed by the elasticity operator with nonlinear, Adv. Appl. Math. Mech., 6 (2014), 191--202
-
[5]
D. Benterki, H. Benseridi, M. Dilmi, Asymptotic behavior of solutions to a boundary value problem with mixed boundary conditions and friction law, Bound. Value Probl., 2017 (2017), 17 pages
-
[6]
6] M. Boukrouche, R. El mir, Asymptotic analysis of non-Newtonian fluid in a thin domain with Tresca law, Nonlinear Anal., 59 (2004), 85--105
-
[7]
M. Boukrouche, G. Lukaszewicz, On a lubrication problem with Fourier and Tresca boundary conditions, Math. Models Methods Appl. Sci., 14 (2004), 913--941
-
[8]
P. G. Ciarlet, Plates and junctions in elastic multi-structures asymptotic analysis, Springer-Verlag, Berlin (1990)
-
[9]
M. Dilmi, Problèmes aux limites obliques et non linéaires pour les équations de Lamé, These de Doctorat, Universite Ferhat Abbes -Setif (2018)
-
[10]
R. El Mir, Comportement asymptotique d’un fluide de Bingham dans un film mince avec des conditions non-lineaires sur le bord, These de Doctorat, France (2006)
-
[11]
M. A. Ezzat, M. I. A. Othman, El-Karamany, The dependence of the modulus of elasticity on the reference temperature in generalized thermoelasticity, J. Thermal Stres., 24 (2001), 1159--1176
-
[12]
Y. Letoufa, H. Benseridi, M. Dilmi, Asymptotic study of a frictionless contact problem between two elastic bodies, J. Math. Computer Sci., 16 (2016), 336--350
-
[13]
J. L. Lions, Quelques méthodes de résolution des problemes aux limites non linéaires, Dunod, Paris (1969)
-
[14]
J.-L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris (1968)
-
[15]
M. Marin, Generalized solutions in elasticity of micropolar bodies with voids, Rev. Acad. Canaria Cienc., 8 (1996), 101--106
-
[16]
M. Marin, An uniqueness result for body with voids in linear thermoelasticity, Rend. Mat. Appl. (7), 17 (1997), 103--113
-
[17]
M. Marin, On the domain of influence in thermoelasticity of bodies with voids, Arch. Math. (Brno), 33 (1997), 301--308
-
[18]
J. Necas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris (1967)
-
[19]
M. I. A. Othman, The uniqueness and reciprocity theorem for generalized thermo-viscoelasticity with thermal relaxation times, Mech. Mech. Eng., 7 (2004), 77--87
-
[20]
M. I. A. Othman, Generalized electromagneto-thermoelastic plane waves by thermal shock problem in a finite sonductivity half-space with one relaxation time, Multidiscip. Model. Materials Struct., 1 (2005), 231--250
-
[21]
M. I. A. Othman, S. Y. Atwa, Response of micropolar thermoelastic solid with voids due to various sources under Green Naghdi theory, Acta Mech. Solida Sinica, 25 (2012), 197--209
-
[22]
A. Saadallah, H. Benseridi, M. Dilmi, S. Drabla, Estimates for the asymptotic convergence of a non-isothermal linear elasticity with friction, Georgian Math. J., 23 (2016), 435--446