Roberta Nibbi

Continuous dependence on modelling for temperature-dependent bidispersive flow

We consider a model for flow in a porous medium which has a double porosity structure. There is the usual porosity herein called macro porosity, but in addition, we allow for a porosity due to cracks or fissures in the solid skeleton. The cracks give rise to a micro porosity. The model considered also allows for temperature effects with a single temperature T. This paper analyses three aspects of structural stability. The first establishes continuous dependence of the solution on the interaction coefficient between the velocities associated with the macro and micro porosity. The second analyses continuous dependence on the viscosity coefficients, while the third establishes continuous dependence on the radiation constant when Newton’s law of cooling is involved on the boundary.

On the asymptotic behavior of the quasi-static problem for a linear viscoelastic fluid

In this paper we study the quasi-static problem for a viscoelastic fluid by means of the concept of minimal state. This implies the use of a different free energy defined in a wider space of data. The existence and uniqueness is proved in this new space and the asymptotic decay for the problem with non vanishing supplies is obtained for a large class of memory kernels, including those presenting an exponential or polynomial decay.

Energy decay in Green–Naghdi thermoelasticity with diffusion and dissipative boundary controls

ABSTRACT 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.