The three-phase-lag model and Green–Naghdi theory without energy dissipation are employed to study the deformation of a two-temperature fiber-reinforced medium with an internal heat source that is moving with a constant speed under a hydrostatic initial stress and the gravity field.  The modulus of the elasticity is given as a linear function of the reference temperature. The exact expressions ...

In this paper, the basic governing equations for isotropic and homogeneous generalized thermoelastic half-space under hydrostatic initial stress are formulated in the context of the Green and Naghdi theory of types II and III. These governing equations are solved analytically to obtain the dimensional velocities in an xy-plane. It is shown that there exist three plane waves, namely a thermal wa...

We introduce a new class of two-dimensional fully nonlinear and weakly dispersive Green-Naghdi equations over varying topography. These new Green-Naghdi systems share the same order of precision as the standard one but have a mathematical structure which makes them much more suitable for the numerical resolution, in particular in the demanding case of two dimensional surfaces. For these new mod...

A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic...

Abstract In our paper, we consider the mixed problem in context of Green-Naghdi theory thermoelastic Cosserat media. Using very accessible mathematical calculations, prove two qualitative results on solutions formulated problem. Thus, first these approaches, obtain a result stability, Hölder type, with regards to loads. second main result, continuous dependence regarding initial values from It ...

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas....

The two-dimensional Green–Naghdi equations are studied for the case of uneven bottom topography. topography function can depend on time. Group classification these with respect to describing is performed using an algebraic approach.