The research interests of prof. Romano concern the following areas:

- Mathematical models and simulations for charge transport in semiconductors;
- Shock wave stability;
- Radiation hydrodynamics;
- Group methods for finding exact solutions;
- Numerical methods for hyperbolic systems;
- Mathematical aspects of relativistic fluidodynamics and applications in astrophysics and cosmology;
- Non-linear waves.

Continuous models has been formulated for charge transport in semiconductors. The balance equations has been deduced by taking the moment of the transport equations while the needed closure relations (for high order fluxes and production terms) have been obtained by the maximum entropy principle.

The nonparabolicity of the energy bands and all the relevant scattering mechanism have been included. In particular, silicon and gallium arsenide have been tackled. Quantum corrections to the semiclassical models have been obtained by an asymptotic expansion of the Wigner transport equation under a suitable scaling which balances the drift and the collision terms, valid at high electric fields.

In the case of structures with confining effects, e.g. in a DG-MOSFET, models have been formulated including the presence of subbands. They have the form of energy-transport systems coupled to the equations of Poisson and Schroedinger.

Since with shrinking of the electron devices thermal effects are becoming more and more inportant, they have been included with hydrodynamical models deduced, in an analogous ways to the done for electrons, starting from the semiclassical phonon transport equations.

For the models mentioned above suitable numerical schemes has been devised and the main electron devices, as MESFET, MOSFET and DG-MOSGET, have been simulated. By employing genetic-type algorithms, it has been also performed an analysis for the optimizations of such devices.

Recently, issues related to charge transpot in graphene have been tackled. Hydordynamical models based on the maximum entropy principle have been formulated. Moreover it has been investigated the numerical solution of the semiclassical transport equations both by a discontinous Galerkin method and by direct simulation Monte Carlo approaches. These lattes, improving the results known in the literature, properly take into account the Pauli exclusion principle. heating effects have been also studied both with hydrodynamic models and Monte Carlo simulations.

A covariant formulation of the theory of flow limiters, previously given by D. Levermore in the classical case for a field of radiation interacting with a static means, has been elaborated, taking into account only isotropic scattering mechanisms.

The general theory has been developed in the case of space-time with an arbitrary metric (obviously compatible with the principles of General Relativity) even in the presence of a non-static means and taking into account anisotropic scatterings. The resulting model is represented by a diffusion equation for the radiative energy density, which, unlike Thomas's classical theory, is parabolic nonlinear.

Applications for the study of perturbation of the cosmic background radiation and applications to Bianchi's cosmological models have been performed.

Jumping conditions for a relativistic radiative gas, described by a variable Eddington factor, have been studied along with the analysis of the shock wave structure in the classical case considering a cold unperturbed state. The study of some mathematical properties (symmetry of equations and good position of Cauchy's problem) has been carried out for the same model, in the case of special relativity, along with a shock wave stability analysis.

A critical review of the principles of relativistic fluid dynamics has been introduced, with particular reference to the case of a radiative gases, and the principle of maximum entropy has been applied to the case of relativistic radiative gases.

A cosmological model of Bianchi of type I has been analyzed, with a dissipative fluid described by the truncated version of the relativistic extended thermodynamics. The same analysis has been extended to a model of Bianchi type III, considering the complete version of the relativistic Extended Thermodynamics. Both analyses show that the presence of bulk viscosity makes de Sitter's universe asymptotically stable in the phase space of Hubble's functions, providing a somewhat natural way of obtaining an inflationary phase in the early stage of the Universe.

Exact solutions to cosmological models with a dissipative fluid in non-homogeneous cases have been also presented under particular hypothesis of space-time symmetry.

Group analysis methos have been applied to system of drift-diffusion and energy-transport type. For such models, in the case of semiconductors, classes of exact solutions have been obtained.