TY  - JOUR
ID  - Dilmi2023
LB  - Dilmi2023
AU  - Dilmi, Mohamed
AU  - Otmani, Sadok
TI  - Existence and asymptotic stability for generalized elasticity equation with variable exponent
ST  - Existence and asymptotic stability for generalized elasticity equation with variable exponent
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 3
SP  - 409
EP  - 428
DO  - https://doi.org/10.7494/OpMath.2023.43.3.409
UR  - https://doi.org/10.7494/OpMath.2023.43.3.409
AB  - 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.
KW  - asymptotic stability
KW  - variable exponent Lebesgue and Sobolev spaces
KW  - generalized elasticity equation
SN  - 1232-9274
ER  -