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Existence and asymptotic stability for generalized elasticity equation with variable exponent

Dilmi Mohamed, Otmani Sadok

Opuscula Mathematica

2023

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.