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Asymptotic analysis for coupled parabolic problem with Dirichlet-Fourier boundary conditions in a thin domain

100%

Dilmi M.

Journal of Mathematics and Applications

2023

tom Vol. 46

163--185

This paper concerns the asymptotic behaviour of the initial boundary value problem of a class of reaction-diffusion systems (coupled parabolic systems) posed in a thin domain with Dirichlet-Fourier boundary conditions. We first prove the existence and uniqueness of the solution to the problem for fixed ε >0 by the Galerkin method. Then, we give the characterization of the limiting behaviour of these solution as the thinness tends to zero.

Existence and asymptotic stability for generalized elasticity equation with variable exponent

63%

Dilmi M. , Otmani S.

tom Vol. 43, no. 3

409--428

In this paper we propose a new mathematical model describing the deformations of an isotropic nonlinear elastic body with variable exponent in dynamic regime. We assume that the stress tensor σp(·) has the form σp(·)(u) =(2μ + |d(u)|p(·)−2) d(u) + λTr (d(u)) I3, where u is the displacement field, μ, λ are the given coefficients d(·) and I3 are the deformation tensor and the unit tensor, respectively. By using the Faedo-Galerkin techniques and a compactness result we prove the existence of the weak solutions, then we study the asymptotic behaviour stability of the solutions.

Source term model for elasticity system with nonlinear dissipative term in a thin domain

51%

Dilmi M. , Dilmi M. , Boulaaras S. , Benseridi H.

Demonstratio Mathematica

2022

tom Vol. 55, nr 1

437--451

This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u∗ is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.