Seminario de Ecuaciones Diferenciales

Sesión doble del seminario de ecuaciones diferenciales:

PRIMER SEMINARIO:
Horario: de 10:00 a 11:00.
Ponente: Alessio Pomponio (Politecnico di Bari).
Título: The Born-Infeld equation: solutions and equilibrium measures.
Abstract:
In this talk, we deal with the following problem (BI)

The equation in (BI) appears for instance in the Born-Infeld nonlinear electromagnetic theory: in the electrostatic case it corresponds to the Gauss law in the classical Maxwell theory and so φ is the electric potential and ρ is an assigned extended charge density. In the first part of the talk, we discuss existence, uniqueness and regularity of the solution of (BI). In the second part, instead, we deal with existence of equilibrium measures ρ∗ , namely distributions that produce least-energy potentials among all the possible charge distributions, and properties of the corresponding equilibrium potentials ϕρ∗ for (BI). The results have been obtained in joint works with Denis Bonheure (Universite libre de Bruxelles, Belgium), Pietro d’Avenia (Politecnico di Bari, Italy) and Wolfgang Reichel (Karlsruher Institut für Technologie, Germany).

SEGUNDO SEMINARIO:
Horario: de 11:00 a 12:00.
Ponente: Maria Clara Grácio (Universidad de Evora).
Título: Synchronization in networks.
Abstract:
We analyze how the behavior of a chaotic dynamic system changes when it is subjected to a coupling. We consider several types of couplings and several free dynamics, analyzing in each situation the evolution of the behavior as a function of the force-coupling constant. We define and delimit behavior windows. If one dynamic system, instead of being coupled to only one other, is connected to several, we are faced with a network of dynamic systems. We have added to this situation some of the results obtained, namely those concerning full synchronization.