Existence and asymptotic stability for generalized elasticity equation with variable exponent

IF 1 Q1 MATHEMATICS
M. Dilmi, Sadok Otmani
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引用次数: 0

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.
变指数广义弹性方程的存在性及渐近稳定性
本文提出了一种描述各向同性变指数非线性弹性体在动力状态下变形的数学模型。我们假设应力张量\(\sigma^{p(\cdot)}\)的形式为\[\sigma^{p(\cdot)}(u)=(2\mu +|d(u)|^{p(\cdot)-2})d(u)+\lambda Tr(d(u)) I_{3},\],其中\(u\)为位移场,\(\mu\), \(\lambda\)为给定系数\(d(\cdot)\)和\(I_{3}\)分别为变形张量和单位张量。利用Faedo-Galerkin技术和一个紧性结果证明了弱解的存在性,然后研究了解的渐近行为稳定性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Opuscula Mathematica
Opuscula Mathematica MATHEMATICS-
CiteScore
1.70
自引率
20.00%
发文量
30
审稿时长
22 weeks
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