Estimates for the asymptotic convergence of a non-isothermal linear elasticity with friction
-
Abdelkader Saadallah
,
Hamid Benseridi
Abstract
In this paper, we are interested in the study of the asymptotic analysis of a dynamical problem in elasticity with nonlinear friction of Tresca type. The Lamé coefficients of a thin layer are assumed to vary with respect to the thin layer parameter ε and to depend on the temperature. We prove the existence and uniqueness of a weak solution for the limit problem. The proof is carried out by the use of the asymptotic behavior when the dimension of the domain tends to zero.
References
[1] Atkinson K. and Han W., Theoretical Numerical Analysis. A Functional Analysis Framework, Texts Appl. Math. 39, Springer, New York, 2001. 10.1007/978-0-387-21526-6Suche in Google Scholar
[2] Bayada G. and Boukrouche M., On a free boundary problem for the Reynolds equation derived from the Stokes systems with Tresca boundary conditions, J. Math. Anal. Appl. 282 (2003), no. 1, 212–231. 10.1016/S0022-247X(03)00140-9Suche in Google Scholar
[3] Bayada G. and Lhalouani K., 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), no. 3–4, 329–362. Suche in Google Scholar
[4] Benseridi H. and Dilmi M., Some inequalities and asymptotic behavior of a dynamic problem of linear elasticity, Georgian Math. J. 20 (2013), no. 1, 25–41. 10.1515/gmj-2013-0004Suche in Google Scholar
[5] Boukrouche M. and El Mir R., Asymptotic analysis of a non-Newtonian fluid in a thin domain with Tresca law, Nonlinear Anal. 59 (2004), no. 1–2, 85–105. 10.1016/j.na.2004.07.003Suche in Google Scholar
[6] Boukrouche M. and El Mir R., 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), no. 2, 674–692. 10.1016/j.nonrwa.2006.12.012Suche in Google Scholar
[7] Boukrouche M. and ukaszewicz G. Ł., On a lubrication problem with Fourier and Tresca boundary conditions, Math. Models Methods Appl. Sci. 14 (2004), no. 6, 913–941. 10.1142/S0218202504003490Suche in Google Scholar
[8] Boukrouche M. and Saidi F., Non-isothermal lubrication problem with Tresca fluid-solid interface law II. Asymptotic behavior of weak solutions, Nonlinear Anal. Real World Appl. 9 (2008), no. 4, 1680–1701. 10.1016/j.nonrwa.2007.05.003Suche in Google Scholar
[9] Duvaut G. and Lions J. L., Les Inéquations en Mécanique et en Physique, Travaux et Recherches Mathématiques 21, Dunod, Paris, 1972. Suche in Google Scholar
[10] Gallouët T. and Herbin R., Existence of a solution to a coupled elliptic system, Appl. Math. Lett. 7 (1994), no. 2, 49–55. 10.1016/0893-9659(94)90030-2Suche in Google Scholar
[11] Girault V. and Raviart P. A., Finite Element Approximation of the Navier–Stokes Equations, Lecture Notes in Math. 749, Springer, Berlin, 1979. 10.1007/BFb0063447Suche in Google Scholar
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Non-trivial solutions for nonlocal elliptic problems of Kirchhoff-type
- Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data
- On the modification of the Szaśz–Durrmeyer operators
- A spectral representation of the linear multivelocity transport problem
- A Tauberian theorem for the product of Abel and Cesàro summability methods
- The spaces of bilinear multipliers of weighted Lorentz type modulation spaces
- Summations of Schlömilch series containing Struve function terms
- On nondifferentiable minimax semi-infinite programming problems in complex spaces
- Modified relativistic Laguerre polynomials. Monomiality and Lie algebraic methods
- On the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector
- The Hardy--Littlewood maximal operator and BLO1/log class of exponents
- Bicritical domination and double coalescence of graphs
- The asymptotic behavior of a counting process in the max-scheme. A discrete case
- Functions of bounded fractional differential variation – A new concept
- Sensitivity analysis of the optimal exercise boundary of the American put option
- Estimates for the asymptotic convergence of a non-isothermal linear elasticity with friction
- A coupled system of nonlinear differential equations involving m nonlinear terms
Artikel in diesem Heft
- Frontmatter
- Non-trivial solutions for nonlocal elliptic problems of Kirchhoff-type
- Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data
- On the modification of the Szaśz–Durrmeyer operators
- A spectral representation of the linear multivelocity transport problem
- A Tauberian theorem for the product of Abel and Cesàro summability methods
- The spaces of bilinear multipliers of weighted Lorentz type modulation spaces
- Summations of Schlömilch series containing Struve function terms
- On nondifferentiable minimax semi-infinite programming problems in complex spaces
- Modified relativistic Laguerre polynomials. Monomiality and Lie algebraic methods
- On the difference between a Vitali–Bernstein selector and a partial Vitali–Bernstein selector
- The Hardy--Littlewood maximal operator and BLO1/log class of exponents
- Bicritical domination and double coalescence of graphs
- The asymptotic behavior of a counting process in the max-scheme. A discrete case
- Functions of bounded fractional differential variation – A new concept
- Sensitivity analysis of the optimal exercise boundary of the American put option
- Estimates for the asymptotic convergence of a non-isothermal linear elasticity with friction
- A coupled system of nonlinear differential equations involving m nonlinear terms
