EXISTENCE AND ASYMPTOTIC STABILITY FOR GENERALIZED ELASTICITY EQUATION WITH VARIABLE EXPONENT

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)(center dot) has the form sigma(p(center dot))(u) = (2 mu + vertical bar d(u)|p((center dot)-2)) d(u) + lambda Tr (d(u)) I-3, where u is the displacement field, mu, lambda are the given coefficients d(center dot) 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.