We study the linear theory of thermo-electro-viscoelasticity Green–Naghdi type for case a one-dimensional body. For corresponding mathematical model, we prove uniqueness theorem solution to mixed boundary-initial-value problem by means Laplace transform after rewriting constitutive equations in an appropriate form. Moreover, derive result continuous dependence upon supply terms.

We consider the design of nite element methods for the Naghdi shell model in the case when the deformation is bending dominated. Two formulations based on stabilizing techniques are introduced and it is proved that they are stable, hence free from locking. The theoretical estimates are connrmed by numerical benchmark studies. M ethodes d' el ements nis stabilis ees pour les coques a exion domin...

We are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order to offer a unified and comprehensive exposition. Anterior models such as the shallow water and Boussinesq systems, as well as unidirectional models of Camass...

We derive here a variant of the 2D Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard 2D GreenNaghdi equations. Its mathematical interest is that it allows a control of the rotational part of the (vertically averaged) horizontal velocity, which is not the case for the usual Green...

In the present research, vibrational behavior of anisotropic protein microtubules (MTs) immersed in cytosol via Cooper–Naghdi shell model is investigated. MTs are hollow cylindrical structures in the eukaryotic cytoskeleton which surrounded by filament network. The temperature effect on vibration frequency is also taken into account by assuming temperature-dependent material properties for MTs....

Abstract We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing thermal convection, analysing these detail, and deriving critical Rayleigh wave numbers the onset convective fluid motion. In addition to linear instability theory we present careful analysis fully nonlinear stability theory. theories analysed all possess bi-Laplacian term n...