Barbara Lazzari

We take up the challenge to explain the correlation between the Jeans instability topic towards star formation within the accelerated expansion of universe and the role of torsional shear-like Alfven waves in triggering the formation of network patterns, by proposing new mathematical models for self-gravitating interstellar non ideal MHD plasmas. The diffusion of the gravitational field is included via a parabolic Einstein’s equation with the cosmological constant, whereas anomalous resistive features are described through non ideal Ohm’s laws incorporating inertia terms, to account of relaxation and retardation magnetic responses. We perform a spectral analysis to test the stability properties of the novel constitutive settings where dissipative and elastic devices act together, by emphasizing the differences with previous models. As a main result, we highlight the definition of a lower critical threshold, here called the Jeans-Einstein wavenumber, against collapse formation towards the formation of longitudinal gravito-magneto-sonic waves and transverse non gravitational Alfven waves exhibiting larger effective wavespeeds, due to the hyperbolic-parabolic diffusion of the magnetic field. Consequently shorter collisional times are allowable so, beyond the plasma-beta, another interesting key point is the definition of the Ohm number to revisit the timescale topic, towards reviewed Reynolds and Lundquist numbers able to better capture the microphysical phenomena of Magnetic Reconnection in narrow diffusion regimes.

This paper studies a model for thermoelasticity where the body has a double porosity structure. There are the usual pores associated to a porous body, herein called macro pores. In addition, the solid skeleton contains cracks or fissures that give rise to a micro porosity. The fully anisotropic situation is analyzed. We firstly establish uniqueness of a solution to the boundary‐initial value problem when the elastic coefficients are sign indefinite and are required to satisfy only major symmetry. Furthermore, in the quasi‐equilibrium case, where the solid acceleration is neglected, we demonstrate that a solution to the boundary‐initial value problem with zero boundary conditions will decay to zero in a certain sense, under the assumption that there are no sources and external body force involved.

In this paper, the seeming inconsistency highlighted by Fabrizio and Lazzari (Stability and second law of thermodynamics in dual-phase-lag heat conduction,

We study the asymptotic behavior of the solutions of a three-dimensional hyperbolic system arising in the Green–Naghdi models of thermoelasticity with diffusion of type-II and III, in the presence of dissipative boundary controls and prove that the energy exponentially decays in time.

In the context of new models of heat conduction, the second-order approximation of Tzou's theory, derived by Quintanilla and Racke, has been studied recently by two of the present authors, where it was proved equivalent to a fading memory material. The importance of determining free energy functionals for such materials, and indeed for any material with memory, is emphasized. Because the kernel does not satisfy certain convexity restrictions that allow us to obtain various traditional free energies for materials with fading memory, it is necessary to restrict the study to the minimum and related free energies, which do not require these restrictions. Thus, the major part of this work is devoted to deriving an explicit expression for the minimum free energy. Simple modifications of this expression also give an intermediate free energy and the maximum free energy for the material. These derivations differ in certain important respects from earlier work on such free energies.

We present a nonlinear model for Johnson–Segalman type polymeric fluids in porous media, accounting for thermal effects of Oldroyd‐B type. We provide a thermodynamic development of the Darcy's theory, which is consistent with the interlacement between thermal and viscoelastic relaxation effects and diffusion phenomena. The appropriate invariant convected time derivative for the flux vector and the stress tensor is discussed. This is performed by investigating the local balance laws and entropy inequality in the spatial configuration, within the single‐fluid approach. For constant parameters, our thermomechanical setting is of Jeffreys type with two delay time parameters, and hence, in the linear/linearized version, it is strictly related to phase‐lag theories within first‐order Taylor approximations.A detailed spectral analysis is carried out for the linearized version of the model, with a scrutiny to some significant limit situations, enhancing the stabilizing effects of the dissipative and elastic mechanisms, also for retardation responses.For polymeric liquids, rheological aspects, wave propagation properties and analogies with other theories with lagging are pointed out. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper we have proved exponential asymptotic stability for the corotational incompressible diffusive Johnson-Segalman viscolelastic model and a simple decay result for the corotational incompressible hyperbolic Maxwell model. Moreover we have established continuous dependence and uniqueness results for the non-zero equilibrium solution.   In the compressible case, we have proved a Hölder continuous dependence theorem upon the initial data and body force for both models, whence follows a result of continuous dependence on the initial data and, therefore, uniqueness.   For the Johnson-Segalman model we have also dealt with the case of negative elastic viscosities, corresponding to retardation effects. A comparison with other type of viscoelasticity, showing short memory elastic effects, is given.