@Article{Dilmi2023,
author = "Dilmi, Mohamed and Otmani, Sadok",
title = "Existence and asymptotic stability for generalized elasticity equation with variable exponent",
journal = "Opuscula Math.",
year = "2023",
volume = "43",
number = "3",
pages = "409--428",
doi = "https://doi.org/10.7494/OpMath.2023.43.3.409",
url = "https://doi.org/10.7494/OpMath.2023.43.3.409",
abstract = "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 \(\sigma^{p(\cdot)}\) has the form \[\sigma^{p(\cdot)}(u)=(2\mu +|d(u)|^{p(\cdot)-2})d(u)+\lambda Tr(d(u)) I_{3},\] where \(u\) is the displacement field, \(\mu\), \(\lambda\) are the given coefficients \(d(\cdot)\) and \(I_{3}\) 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.",
keywords = "asymptotic stability, variable exponent Lebesgue and Sobolev spaces, generalized elasticity equation",
issn = "1232-9274"
}