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“My 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 my PhD I have 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, I am getting interested in non-local transport problems, derived from models of collection behaviour.”
- PhD summa cum laude in Mathematics (Sep 2013 – Dec 2016), University of the Basque Country and BCAM – Basque Center for Applied Mathematics, Bilbao, Spain.
- Internship (Mar 2013 – Aug 2013), BCAM – Basque Center for Applied Mathematics, Bilbao, Spain, ERC Advanced Grant FP7-246775 NUMERIWAVES.
- Master degree in applied mathematics (2010 – 2012), University of Florence, Italy.
- Bachelor’s Degree in Mathematics (2007 – 2010), University of Florence, Italy.
On the controllability of Partial Differential Equations involving non-local terms and singular potentials
Advisor: Prof. Enrique Zuazua – Universidad Autónoma de Madrid and DeustoTech – University of Deusto – Bilbao, Spain
Description: In this thesis we study the controllability and observability of certain types of Partial Differential Equations, that describes several phenomena arising in many fields of the applied sciences, such as elasticity theory, ecology, anomalous transport and diffusion, material science, filtration in porus media and quantum mechanics. In particular, we focus on the analysis of PDEs with non-local and singular terms.
A free boundary problem for the neutralisation of acid waters
Advisors: Prof. Riccardo Ricci and Dr. Angiolo Farina – University of Florence, Italy.
Description: In this thesis is analysed a parabolic free boundary model arising from a problem of neutralization of acid waters via the filtration through calcium carbonate. After having developed the model according to the Physics, it has been computed an approximate solution, analysing its properties and its asymptotic behaviour. This analysis has been repeated also in cylindrical and spherical geometry.
- Biccari U., Zuazua E. Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function Journal of Differential Equations
- Biccari U., Warma M., Zuazua E. Local elliptic regularity for the Dirichlet fractional Laplacian Advanced Nonlinear Studies 17 (2017), 387-409.
- Biccari U. Internal control for non-local Schrödinger and wave equations involving the fractional Laplace operator (Submitted)
- Biccari U., Warma M. Boundary null controllability for a heat equation with general dynamical boundary condition. (Submitted)
- Biccari U., Warma M. and Zuazua E. Local regularity for fractional heat equations (Submitted)
- Biccari U. Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential (Submitted)
- Biccari U., Hernández-Santamaría V. A finite element approximation of the one-dimensional fractional Poisson equation with applications to numerical control (Submitted)