Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-28T03:26:21.161Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic Study of a Boundary Value Problem Governed by the Elasticity Operator with Nonlinear Term

Published online by Cambridge University Press:  03 June 2015

D. Benterki ,
H. Benseridi  and
M. Dilmi
D. Benterki*
Affiliation:
Applied Mathematics Laboratory, BB-University, 34000, Algeria
H. Benseridi*
Affiliation:
Applied Mathematics Laboratory, Department of Mathematics, Setif I-University, 19000, Algeria
M. Dilmi*
Affiliation:
Applied Mathematics Laboratory, Department of Mathematics, M’sila University, 28000, Algeria
*
Email: benterkidj@yahoo.fr
Corresponding author. Email: m_benseridi@yahoo.fr
Email: mouraddil@yahoo.fr
Get access

Abstract

In this paper, a nonlinear boundary value problem in a three dimensional thin domain with Tresca’s friction law is considered. The small change of variable z = x3/ε transforms the initial problem posed in the domain Ωε into a new problem posed on a fixed domain Ω independent of the parameter ε. As a main result, we obtain some estimates independent of the small parameter. The passage to the limit on ε, permits to prove the results concerning the limit of the weak problem and its uniqueness.

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 2 , April 2014 , pp. 191 - 202
Copyright
Copyright © Global-Science Press 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bayada, G. and Boukrouche, M., On a free boundary problem for Reynolds equation derived from the Stokes system with Tresca boundary conditions, J. Math. Anal. Appl., 382 (2003), pp. 212–231.CrossRefGoogle Scholar
[2]Benseridi, H. AND Dilmi, M., Some inequalities and asymptotic behaviour of dynamic problem of linear elasticity, Georgian Math. J., 20(1) (2013), pp. 25–41, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: 10.1515/gmj-2013-0004,March 2013.Google Scholar
[3]Boukrouche, M. and Mir, R. El, Asymptotic analysis of non-Newtonian fluid in a thin domain with Tresca law, Nonlinear Anal. Theory Methods Appl., 59 (2004), pp. 85–105.Google Scholar
[4]Boukrouche, M. and Lukaszewicz, G., On a lubrication problem with Fourier and Tresca boundary conditions, Math. Models Methods Appl. Sci., 14(6) (2004), pp. 913–941.Google Scholar
[5]Dilmi, M., Benseridi, H. AND Saadallah, A., Asymptotic Behaviour of a Nonlinear Boundary Value Problem with Friction, submitted for publication in J, Georgian Math..Google Scholar
[6]Duvaut, G. AND Lions, J. L., Les Inequations en MeCanique des Fluides, Dunod, 1969.Google Scholar
[7]Lions, J. L., Quelques methodes de résolution des problemes aux limites non linéaires, Paris, Dunod, (1969).Google Scholar
[8]Lions, J. L. et Magenes, E., Problèmes aux limites non homogènes et applications, Vol. 2, Paris, Dunod, (1968).Google Scholar
[9]Rahmoune, A. AND Benabderrahmane, B., Faedo-Galerkin’s method for a non linear boundary value problem, Int. J. Open Problems Comput. Math., 4(4) (2011).Google Scholar
[10]Saadallah, A., Benseridi, H. AND Dilmi, M., Asymptotic analysis of a dynamical problem of non-isothermal linear elasticity with friction, to appear in Acta Mathematicae Applicatae Sinica, English Series, ISSN: 0168-9673.Google Scholar