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Volume 6, Issue 2
Asymptotic Study of a Boundary Value Problem Governed by the Elasticity Operator with Nonlinear Term

D. Benterki, H. Benseridi & M. Dilmi

DOI: 10.4208/aamm.2013.m207

Adv. Appl. Math. Mech., 6 (2014), pp. 191-202.

Published online: 2014-06

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  • 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.

  • Keywords

A priori inequalities, free boundary problems, nonlinear operator, Tresca law, variational problem.

  • AMS Subject Headings

35R35, 76F10, 78M35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-191, author = {Benterki , D.Benseridi , H. and Dilmi , M.}, title = {Asymptotic Study of a Boundary Value Problem Governed by the Elasticity Operator with Nonlinear Term}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {2}, pages = {191--202}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m207}, url = {http://global-sci.org/intro/article_detail/aamm/13.html} }
TY - JOUR T1 - Asymptotic Study of a Boundary Value Problem Governed by the Elasticity Operator with Nonlinear Term AU - Benterki , D. AU - Benseridi , H. AU - Dilmi , M. JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 191 EP - 202 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m207 UR - https://global-sci.org/intro/article_detail/aamm/13.html KW - A priori inequalities, free boundary problems, nonlinear operator, Tresca law, variational problem. AB -

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.

D. Benterki, H. Benseridi & M. Dilmi. (1970). Asymptotic Study of a Boundary Value Problem Governed by the Elasticity Operator with Nonlinear Term. Advances in Applied Mathematics and Mechanics. 6 (2). 191-202. doi:10.4208/aamm.2013.m207
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