On a pure traction problem for the nonlinear elasticity system in Sobolev spaces with variable exponents

Zoubai Fayrouz; Merouani Boubakeur

doi:10.24193/subbmath.2022.1.12

Authors

Zoubai Fayrouz Setif 1 University, Department of Mathematics, Applied Mathemathics Laboratory (LaMA).
Merouani Boubakeur Setif 1 University, Department of Mathematics, Applied Mathemathics Laboratory (LaMA).

DOI:

https://doi.org/10.24193/subbmath.2022.1.12

Keywords:

Spaces of Lebesgue and Sobolev with variable exponents, Nonlinear Elasticity System, Operator of Leray-Lions, Existence, Uniqueness, Neumann problem

Abstract

One can find in the literature several authors who studied the system of
elasticity with laws of particular behavior and using various techniques in constant exponents Sobolev spaces. In this article we consider a Neumann problem for nonlinear elasticity system with laws of general behavior. The coefficients of elasticity depends on x and the density of the volumetric forces depends on the displacement. We consider this problem as a Leray-Lions operator and the main aim of this paper is to apply Galerkin techniques and monotone operator theory to prove a theorem of existence and uniqueness.

Author Biographies

Zoubai Fayrouz, Setif 1 University, Department of Mathematics, Applied Mathemathics Laboratory (LaMA).

Setif-19000
Merouani Boubakeur, Setif 1 University, Department of Mathematics, Applied Mathemathics Laboratory (LaMA).

Setif-19000

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