Mathematical Contributions to the Dynamics of the Josephson Junctions: State of the Art and Open Problems

Mathematical models related to some Josephson junctions are pointed out and attention is drawn to the solutions of certain initial boundary problems and to some of their estimates. In addition, results of rigorous analysis of the behaviour of these solutions when the time tends to infinity and when the small parameter tends to zero are cited. These analyses lead us to mention some of the open problems.Comment: 11 page

GLAST, the Gamma-ray Large Area Space Telescope

GLAST, a detector for cosmic gamma rays in the range from 20 MeV to 300 GeV, will be launched in space in 2005. Breakthroughs are expected in particular in the study of particle acceleration mechanisms in space and of gamma ray bursts, and maybe on the search for cold dark matter; but of course the most exciting discoveries could come from the unexpected.Comment: 6 pages, 3 figures. Invited talk at the hird International Workshop "New Worlds in Astroparticle Physics", September 2000, University of the Algarve. Faro, Portugal. To be published in the Proceeding

On the transition from parabolicity to hyperbolicity for a nonlinear equation under Neumann boundary conditions

An integro differential equation which is able to describe the evolution of a large class of dissipative models, is considered. By means of an equivalence, the focus shifts to the perturbed sine- Gordon equation that in superconductivity finds interesting applications in multiple engineering areas. The Neumann boundary problem is considered, and the behaviour of a viscous term, defined by a high order derivative with small diffusion coefficient , is investigated. The Green function, expressed by means of Fourier series, is considered, and an estimate is achieved. Furthermore, some classes of solutions of the hyperbolic equation are determined, proving that there exists at least one solution with bounded derivatives. Results obtained prove that diffusion effects are bounded and tend to zero when e tends to zero.Comment: Meccanica (2018). arXiv admin note: text overlap with arXiv:1602.0907

A wave equation perturbed by viscous terms: fast and slow times diffusion effects in a Neumann problem

A Neumann problem for a wave equation perturbed by viscous terms with small parameters is considered. The interaction of waves with the diffusion effects caused by a higher-order derivative with small coefficient {\epsilon}, is investigated. Results obtained prove that for slow time {\epsilon}t < 1 waves are propagated almost undisturbed, while for fast time t > 1 {\epsilon} diffusion effects prevail.Comment: Ricerche di Matematica (2018

Fundamental Physics With Cosmic High-Energy Gamma Rays

High-energy photons (above the MeV) are a powerful probe for astrophysics and for fundamental physics under extreme conditions. During the recent years, our knowledge of the high-energy gamma-ray sky has impressively progressed thanks to the advent of new detectors for cosmic gamma rays, at ground (H.E.S.S., MAGIC, VERITAS, HAWC) and in space (AGILE, Fermi). This presentation reviews the present status of the studies of fundamental physics problems with high-energy gamma rays, and discusses the expected experimental developments.Comment: Invited Talk at the 6th International Symposium on High-Energy Gamma-Ray Astronomy (Gamma2016), Heidelberg, July 201