Umberto Biccari is a PhD. Currently he holds a Postdoctoral position at the ERC Advanced Grant project DyCon under the supervision of Prof. Enrique Zuazua (UAM and DeustoTech). In the past, he collaborated within the ERC research project NUMERIWAVES. His current research interests are related to the analysis of Partial Differential Equations, in particular from the point of view of control theory. During the years of his PhD he has been concerned with the study of controllability properties of hyperbolic (waves), parabolic (heat) and dispersive (Schrödinger) PDEs, involving non-local terms, singular inverse-square potentials, variable degenerate coefficients or dynamical boundary conditions. At the moment, he is getting interested in non-local transport problems, derived from models of collection behaviour.
Stability analysis of a simplified model for Power Electronic Converters Connected to AC Grids in dependence on the characteristical physical parameters.
Sincronization of coupled oscillator described by the Kuramoto model, using the Stochastic Conjugate Gradient Method
Solution of a fractional Schordinger equation starting from a concentrated and highly oscillatory initial datum, and display of its propagation properties along the rays of geometric optics
Theoretical and numerical analysis of the propagation of the solutions for a Schrödinger equation with fractional Laplacian, with application to the study of controllability properties.
A finite element approximation of the one-dimensional fractional Poisson equation with applications to numerical control
Design of a LQR controller for the stabilization of a fractional reaction diffusion equation