From June 24th to June 28th, 2019, Umberto Biccari visited the Department of Mathematics “Renato Caccioppoli” in Naples, Italy. In that occasion, he taught the intensive course “Control problems for non-local PDEs”, within the framework of INDAM Intensive Period on “Shape optimization, control and inverse problems for PDEs” (webpage).
The course presented a complete overview of Umberto Biccari’s results on controllability properties for non-local PDEs. It was structured into four lectures:
- Introduction to PDE control theory and to non-local models.
- Controllability of fractional hyperbolic and dispersive equations.
- Controllability of fractional parabolic equations.
- Controllability of general non-local equations.
During his stay in Naples, Umberto Biccari had discussions with Giuseppe Floridia on the bilinear control for PDE and on the possibility of extending Floridia’s work to non-local model. The discussion defined the basis for future collaborations between the DyCon team and the University of Naples.