Ricerc@Sapienza

We study a concentration and homogenization problem modelling electrical conduction in a composite material. The novelty of the problem is due to the specific scaling of the physical quantities characterizing the dielectric component of the composite. This leads to the appearance of a peculiar displacement current governed by a Laplace-Beltrami pseudo-parabolic equation. This pseudo-parabolic character is present also in the homogenized equation, which is obtained by the unfolding technique.

We will present some existence and uniqueness theorems for two different two-scale problems ([1]). In this framework, a two-scale problem is a system of PDEs involving two unknowns (u; u_1), the first one just depending on a set of space variables denoted by x (usually called the macroscopic or slow variables) and on the time t, the second one depending on a second set of spatial variables y, beside the old ones (i.e. u_1 depends on (x; y; t)). The second set of space variables y are usually called microscopic or fast variables.

We prove existence and homogenization results for a family (depending on a small parameter and on a parameter 2 f1; 0; 1g) of elliptic problems involving a singular lower order term and representing the Euler equations of energy functionals, which can be used to describe the equilibrium for the heat conduction in composite materials with two finely mixed phases having a microscopic periodic structure (for details on the related physical models see for instance [3, 4] and the reference quoted there).

In this paper we prove an error estimate for a model of heat conduction in composite materials having a microscopic structure arranged in a periodic array and thermally active membranes separating the heat conductive phases.

We prove existence and homogenization results for a family of elliptic problems involving interfaces and a singular lower order term.
These problems model heat or electrical conduction in composite media.

In this paper we prove existence and uniqueness for a parabolic and a parabolic/elliptic two-scale system of partial differential equations typically arising in homogenization theory or in macroscale-microscale applied models.

We prove existence and homogenization results for elliptic problems involving a singular lower order term and defined on a domain with interfaces
having a nonlinear response. The considered system of equations can model heat or electrical conduction in composite media.

This paper concerns the periodic homogenization of the stationary heat equation in a domain with two connected components, separated by an oscillating interface defined on prefractal Koch type curves. The problem depends both on the parameter ? that defines the periodic structure of the interface and on n, which is the index of the prefractal iteration. First, we study the limit as ? vanishes, showing that the homogenized problem is strictly dependent on the amplitude of the oscillations and the parameter appearing in the transmission condition.

We consider the homogenization of a parabolic problem in a perforated domain with Robin–Neumann boundary conditions oscillating in time. Such oscillations must compensate the blow up of the boundary measure of the holes. We use the technique of time-periodic unfolding in order to obtain a macroscopic parabolic problem containing an extra linear term due to the absorption determined by the Robin condition.

We extend the recent technique of the unfolding operator to the case of a time-depending setting.
We apply this technique to the homogenization of parabolic problems with time-depending oscillating coefficients.