Asymptotic behavior for the elasticity system with a nonlinear dissipative term

We study the asymptotic behavior of an elasticity problem with a nonlinear dissipative term in a bidimensional thin domain Ωε. We prove some convergence results when the thickness tends to zero. The specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained

Asymptotic behavior of solutions to a boundary value problem with mixed boundary conditions and friction law

Abstract In this paper, we consider a non-linear problem in a stationary regime in a three-dimensional thin domain Ω ε $\Omega^{\varepsilon}$ with Fourier and Tresca boundary conditions. In the first step, we derive a variational formulation of the mechanical problem. We then study the asymptotic behavior in the one dimension case when the domain parameter tends to zero. In the latter case, a specific Reynolds equation associated with variational inequalities is obtained and the uniqueness of the limit velocity and pressure are proved

Study of a Transmission Problem with Friction Law and Increasing Continuous Terms in a Thin Layer

The aim of this paper is to establish the asymptotic analysis of nonlinear boundary value problems. The non-stationary motion is given by the elastic constructive law. The contact is described with a version of Tresca’s law of friction. A variational formulation of the model, in the form of a coupled system for the displacements and the nonlinear source terms, is derived. The existence of a unique weak solution of the model is established. We also give the problem in transpose form, and we demonstrate different estimates of the displacement and of the source term independently of the small parameter. The main corresponding convergence results are stated in the different theorems of the last section

Исследование проблемы неизотермической связи со смешанными граничными условиями в тонком домене с законом трения

This paper deals with the asymptotic behavior of a coupled system involving of an incompressible Bing- ham fluid and the equation of the heat energy, in a three-dimensional bounded domain with Tresca free boundary friction conditions. First we prove the existence and uniqueness results for the weak solution. Second, we show the strong convergence of the velocity and the temperature. Then a specific Reynolds limit equation is obtained, and the uniqueness of the limit velocity and temperature are proved.В настоящей работе рассматривается асимптотическое поведение связанной системы с несжимаемой жидкостью Бингхэма и уравнения тепловой энергии в трехмерной ограниченной области с условиями свободного трения Треска. Во-первых, мы доказываеме результаты существования и единственности для слабого решения. Во-вторых, мы показываем сильную сходимость скорости и температуры. Затем получаем конкретное предельное уравнение Рейнольдса и доказываем единственность предельной скорости и температур

Abstracts of 1st International Conference on Computational & Applied Physics

This book contains the abstracts of the papers presented at the International Conference on Computational & Applied Physics (ICCAP’2021) Organized by the Surfaces, Interfaces and Thin Films Laboratory (LASICOM), Department of Physics, Faculty of Science, University Saad Dahleb Blida 1, Algeria, held on 26–28 September 2021. The Conference had a variety of Plenary Lectures, Oral sessions, and E-Poster Presentations. Conference Title: 1st International Conference on Computational & Applied PhysicsConference Acronym: ICCAP’2021Conference Date: 26–28 September 2021Conference Location: Online (Virtual Conference)Conference Organizer: Surfaces, Interfaces, and Thin Films Laboratory (LASICOM), Department of Physics, Faculty of Science, University Saad Dahleb Blida 1, Algeria