Francesca Passarella

Some Results in Linear Theory of Thermoelasticity Backward in Time for Microstretch Materials

In this paper the uniqueness of solutions for the backward in time problem of the linear theory of thermo-microstretch elastic materials is shown and the impossibility of the localization in time of the solution of the corresponding forward in time problem is proved. Moreover, the temporal behavior backward in time of thermoelastodynamics processes is studied by establishing the relations describing the asymptotic behavior of the Cesàro means of the different parts of the total energy.

Some Exponential Decay Estimates for Thermoelastic Mixtures

This paper concerns the study of time-harmonic vibrations for some classes of homogeneous and isotropic thermoelastic mixtures for which the constitutive coefficients are supposed to satisfy some mild positive definiteness conditions. Introducing some appropriate measures, we evaluate the spatial decay behaviour, when the frequency of harmonic vibrations is lower than a certain critical value.

SPATIAL BEHAVIOR IN DYNAMICAL THERMOELASTICITY BACKWARD IN TIME FOR POROUS MEDIA

The aim of this paper is to study the spatial behavior of the solutions to the final-boundary-value problems associated with the linear theory of elastic materials with voids. More precisely, the present study is devoted to porous materials with a memory effect for the intrinsic equilibrated body forces. An appropriate time-weighted volume measure is associated with the backward-in-time thermoelastic processes. Then a first-order partial differential inequality in terms of such measure is established and it is further shown how the inequality implies the spatial exponential decay of the thermoelastic process in question.

SAINT-VENANT'S PRINCIPLE IN DYNAMIC POROUS THERMOELASTIC MEDIA WITH MEMORY FOR HEAT FLUX

In the present paper, we study a linear thermoelastic porous material with a constitutive equation for heat flux with memory. An approximated theory of thermodynamics is presented for this model and a maximum pseudofree energy is determined. We use this energy to study the spatial behavior of the thermodynamic processes in porous materials. We obtain the domain-of-influence theorem and establish the spatial decay estimates inside of the domain of influence. Furthermore, we prove a uniqueness theorem valid for finite or infinite bodies. The body is free of any kind of a priori assumptions concerning the behavior of solutions at infinity.

On the Uniqueness in Dynamical Thermoelasticity Backward in Time for Porous Media

The aim of this article is to study some uniqueness criteria for the solutions of boundary-final value problems associated with the linear theory of thermoelastic materials with voids. More precisely, the present study is devoted to the investigation of a backward in time problem associated with porous thermoelastic materials.

Fundamental solutions in antiplane elastodynamic problem for anisotropic medium under moving oscillating source

In present article we consider the problems of concentrated point force which is moving with constant velocity and oscillating with cyclic frequency in unbounded homogeneous anisotropic elastic two-dimensional medium. The properties of plane waves and their phase, slowness and ray or group velocity curves for 2D problem in moving coordinate system are described. By using the Fourier integral transform techniques and established the properties of the plane waves, the explicit representation of the elastodynamic Greens tensor is obtained for all types of source motion as a sum of the integrals over the finite interval. The dynamic components of the Greens tensor are extracted. The stationary phase method is applied to derive an asymptotic approximation of the far wave field. The simple formulae for Poynting energy flux vectors for moving and fixed observers are presented too. It is noted that in the far zones the cylindrical waves are separated under kinematics and energy. It is shown that the motion bring some differences in the far field properties. They are modification of the wave propagation zones and their number, fast and slow waves appearance under trans- and superseismic motion and so on.

On the Heat-Flux Dependent Thermoelasticity for Micropolar Porous Media

In the present paper, in the context of the linear theory of heat-flux dependent thermoelasticity for micropolar porous media, we derive a uniqueness theorem with no positive definiteness assumption on the elastic constitutive coefficients. Moreover, we prove, under non homogeneous initial conditions, a reciprocal relation and a variational principle. These generalize previous results about inhomogeneous and anisotropic micropolar thermoelastic materials.

On the Theory of Micropolar Thermoelasticity without Energy Dissipation

The present paper deals with micropolar thermoelastic materials with a center of symmetry, investigated through the so-called thermoelasticity of type II or thermoelasticity without energy dissipation, which allows propagation of thermal waves at finite speed. In particular, for such a model, a uniqueness theorem, two variational principles (of Hamilton and Biot types, respectively) and a reciprocity result are derived.

Some results in the dynamics of porous elastic mixtures

The present work describes a method for studying the spatial and temporal behaviour of the dynamic processes in porous elastic mixtures taking into account memory effects for the intrinsic equilibrated body forces. The method is based on a set of properties for an appropriate time-weighted surface power function associated with the process at issue. We get the domain of influence and the spatial decay estimates with time-independent decay rate inside the domain of influence. We establish the spatial decay estimates with time-independent decay rate for the interior of the domain of influence. Using the Cesaro means associated with the kinetic and strain energies, we establish the asymptotic partition of the total energy.

On the Spatial and Temporal Behavior in Dynamics of Porous Elastic Mixtures

In this paper, we study the spatial and temporal behavior of dynamic processes in porous elastic mixtures. For the spatial behavior, we use the time-weighted surface power function method in order to obtain a more precise determination of the domain of influence and establish spatial-decay estimates of the Saint-Venant type with respect to time-independent decay rate for the inside of the domain of influence. For the asymptotic temporal behavior, we use the Cesáro means associated with the kinetic and strain energies and establish the asymptotic equipartition of the total energy. A uniqueness theorem is proved for finite and infinite bodies, and we note that it is free of any kind of a priori assumptions on the solutions at infinity.