Study of a boundary value problem governed by the general elasticity system with a new boundary conditions in a thin domain-Reference-Cited by-同舟云学术

Study of a boundary value problem governed by the general elasticity system with a new boundary conditions in a thin domain

Published:2024-08-03 Issue: Volume: Page:
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Boulaouad Abla¹,Djenaihi Youcef¹,Boulaaras Salah²,Benseridi Hamid¹,Dilmi Mourad¹

Affiliation:

1. Laboratory of Applied Mathematics , Faculty of Sciences , University Ferhat Abbas of Sétif 1 , Setif , Algeria

2. Department of Mathematics , College of Science , Qassim University , Buraydah 51452 , Saudi Arabia

Abstract

Abstract The aim of this work is the study of a nonlinear boundary value problem which theoretically generalizes the Lamé system with disturbance in a thin 3D domain with friction and a generalized boundary condition. For the resolution of the considered problem and after the variational formulation, we construct an operator from the variational problem. Then we prove that this operator has certain properties which allows us to apply the theorem of existence and uniqueness of the solution of variational inequalities of the 2nd kind. Finally, using a change of scale, we transport the variational problem to an equivalent problem defined on a domain independent of the parameter ζ

and subsequently we obtain the limit problem and the generalized weak equations of the initial problem.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2024-2044/pdf

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