The present paper deals with the study of the amplitude of the steady-state vibrations in a right finite cylinder made of an isotropic Kelvin-Voigt material. Some exponential decay estimates, similar to those of Saint-Venant type, are obtained for appropriate cross-sectional area measures associated with the amplitude of the steady-state vibrations. It is proved that due to dissipative effects, the estimates in question hold for every value of the

The present article studies some qualitative properties of solutions in the dynamics of viscoelastic mixtures made by two constituents: a porous elastic solid and a viscous fluid. In this sense, some results concerning the theory of semigroups of linear operators are used to establish the existence and uniqueness of the weak solutions of the initial boundary value problems associated with the linear theory. The continuous dependence problem upon

The Cesaro means of various parts of the total energy are introduced in the context of the linear theory of swelling porous elastic media. Then, the relations describing the asymptotic behaviour of the Cesaro means are established.

This paper is concerned with the study of the amplitude of the steady-state vibration in a right finite cylinder made of a mixture consisting of three components: an elastic solid, a viscous fluid and a gas. An exponential decay estimate of Saint-Venant type in terms of the distance from one end of the cylinder is obtained from a first-order differential inequality for a cross-sectional area measure associated with the amplitude of the steady-state

We derive a nonlinear theory of heat-conducting micropolar mixtures in Lagrangian description. The kinematics, balance laws, and constitutive equations are examined and utilized to develop a nonlinear theory for binary mixtures of micropolar thermoelastic solids. The initial boundary value problem is formulated. Then, the theory is linearized and a uniqueness result is established.

This paper is concerned with the study of spatial behavior of solutions in a heat-conducting viscoelastic mixture consisting of two constituents: a porous elastic solid and a viscous fluid. By using adequate time-weighted integral measures, some spatial estimates of Saint-Venant type (for bounded bodies) and Phragmeacuten-Lindeloumlf type (for unbounded bodies) are established. The estimates in question are characterized both by time-independent

A nonlinear theory is developed for a heat-conducting viscoelastic composite which is modelled as a mixture consisting of a microstretch Kelvin-Voigt material and a microstretch elastic solid. The strain measures, the basic laws and the constitutive equations are established and presented in Lagrangian description. The initial boundary value problem associated to such model is also formulated. Then the linearized theory is considered and the constitutive

This paper is concerned with the study of asymptotic spatial behaviour of solutions in a mixture consisting of two thermoelastic solids. A second-order differential inequality for an adequate volumetric measure and the maximum principle for solutions of the one-dimensional heat equation are used to establish a spatial decay estimate of solutions in an unbounded body occupied by the mixture. For a fixed time, the result in question proves that the

This paper deals with the isothermal linear theory of swelling porous elastic soils in the case of fluid saturation. Internal and external boundary value problems of steady vibrations are investigated using the potential method. The uniqueness and existence theorems of classical solutions of the aforementioned problems are proved.

Complete solutions of the field equations in the isothermal linear theory of swelling porous elastic soils in the case of fluid saturation or gas saturation are given. Then a study of the plane waves, Rayleigh waves and fundamental solutions for steady vibrations are presented.