On the asymptotic study of transmission problem in a thin domain

References

[1] C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities: Applications to Free-Boundary Problems, John Wiley, Chichester, 1984. Search in Google Scholar

[2] G. Bayada and M. Boukouche, On a free boundary problem for Reynolds equation derived from the Stokes system with Tresca boundary conditions, J. Math. Anal. Appl. 382 (2003), 212–231. 10.1016/S0022-247X(03)00140-9Search in Google Scholar

[3] G. Bayada and K. Lhalouani, Asymptotic and numerical analysis for unilateral contact problem with Coulomb’s friction between an elastic body and a thin elastic soft layer, Asymptot. Anal. 25 (2001), 329–362. Search in Google Scholar

[4] A. Benseghir, Existence and exponential decay of solutions for transmission problems with delay, Electron. J. Differential Equations 212 (2014), 1–11. Search in Google Scholar

[5] H. Benseridi and M. Dilmi, Some inequalities and asymptotic behavior of dynamic problem of linear elasticity, Georgian Math. J. 20 (2013), no. 1, 25–41. 10.1515/gmj-2013-0004Search in Google Scholar

[6] M. Boukrouche and R. El Mir, Asymptotic Analysis of non-Newtonian fluid in a thin domain with Tresca law, Nonlinear Anal. 59 (2004), 85–105. 10.1016/S0362-546X(04)00248-2Search in Google Scholar

[7] M. Boukrouche and R. El Mir, On a non-isothermal, non-Newtonian lubrication problem with Tresca law: Existence and the behavior of weak solutions, Nonlinear Anal. Real World Appl. 9 (2008), 674–692. 10.1016/j.nonrwa.2006.12.012Search in Google Scholar

[8] M. Boukrouche and G. Lukaszewicz, On a lubrication problem with Fourier and Tresca boundary conditions, Math. Models Methods Appl. Sci. 14 (2004), no. 6, 913–941. 10.1142/S0218202504003490Search in Google Scholar

[9] M. Boukrouche and F. Saidi, Non-isothermal lubrication problem with Tresca fluid-solid interface law, Nonlinear Anal. Real World Appl. 7 (2006), 145–1166. 10.1016/j.nonrwa.2005.10.008Search in Google Scholar

[10] H. Brézis, Equations et inéquations non linéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier 18 (1968), 115–175. 10.5802/aif.280Search in Google Scholar

[11] M. Dilmi, H. Benseridi and A. Saadallah, Asymptotic analysis of a Bingham fluid in a thin domain with Fourier and Tresca boundary conditions, Adv. Appl. Math. Mech. 6 (2014), 797–810. 10.4208/aamm.2013.m350Search in Google Scholar

[12] G. Duvaut and J-L. Lions, Les Inéquations en Mécanique et en Physique, Trav. Math. 21, Dunod, Paris, 1972. Search in Google Scholar

[13] N. Hemici and A. Matei, A frictionless contact problem with adhesion between two elastic bodies, An. Univ. Craiova Ser. Mat. Inform. 30 (2003), no. 2, 90–99. Search in Google Scholar

[14] H. Irago, J. M. Viaño and A. Rodríguez-Arós, Asymptotic derivation of frictionless contact models for elastic rods on a foundation with compliance, Nonlinear Anal. Real World Appl. 14 (2013), 852–866. 10.1016/j.nonrwa.2012.08.006Search in Google Scholar

[15] R. Labbas, K. Lemrabet, K. Limam, A. Medeghri and M. Meisner, On some transmission problems set in a biological cell, analysis and resolution, J. Differential Equations 259 (2015), no. 7, 2695–2731. 10.1016/j.jde.2015.04.002Search in Google Scholar

[16] Y. Letoufa, H. Benseridi and M. Dilmi, Asymptotic study of a frictionless contact problem between two bodies, J. Math. Comput. Sci. 16 (2016), no. 3, 336–350. 10.22436/jmcs.016.03.04Search in Google Scholar

[17] M. Sofonea and A. Matei, Variational Inequalities with Applications. A Study of Anti-plane Frictional Contact Problems, Adv. Mech. Math., Springer, New York, 2009. 10.1007/978-0-387-87460-9_4Search in Google Scholar

[18] M. Sofonea and A. Matei, Mathematical Models in Contact Mechanics, London Math. Soc. Lecture Note Ser., Cambridge University Press, Cambridge, 2012. 10.1017/CBO9781139104166Search in Google Scholar