Postdoctoral Researcher
My primary field of expertise is the analysis of Partial Differential Equations, both from the theoretical and from the numerical point of view, with a particular emphasis on non-local models and control theory.

My primary field of expertise is the analysis of Partial Differential Equations, both from the theoretical and from the numerical point of view, with a particular emphasis on non-local models and control theory. My contributions to the topic spread among different areas of PDE analysis, including:

  • The study of controllability properties of hyperbolic, parabolic and dispersive PDE, involving the
    fractional Laplacian, integral kernels, singular inverse-square potentials and/or variable degenerate
    coefficients, memory terms.
  • Numerical controllability for non-local parabolic PDE involving the fractional Laplacian.
  • Regularity results for non-local elliptic and parabolic PDE involving the fractional Laplacian.
  • Mathematical and numerical asymptotic analysis for the propagation of solutions of wave-like
    processes in a local and non-local setting.
  • Analysis and control of collecting behavior models and their micro-macro limit.

Besides, I am working on the development of mathematical and computational tools for the model, stability analysis, and control of hybrid AC/DC power grids. This is the core topic of two shared research project between our team, the University of Mondragón (Basque Country), and three industrial partners strongly committed with the topics of control and energy management.

  • Ph. D 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.

PhD’s Thesis. On the controllability of Partial Differential Equations involving non-local terms and singular potentials

Advisor: Prof. Enrique Zuazua – FAU (Erlangen-Nürnberg, Germany), Deusto Foundation-University of Deusto (Bilbao, Basque Country, Spain) and UAM (Madrid, 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. View the PhD thesis

Master’s Thesis. A free boundary problem for the CaCO3 neutralisation of acid waters

Advisors: Prof. Riccardo Ricci and Dr. Angiolo Farina – University of Florence, Italy

Description: In this thesis, we analyze 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, we computed an approximate but reliable solution, investigating its properties and its asymptotic behavior. This analysis has been repeated also in cylindrical and spherical geometry, both configurations being relevant in the description of the physical phenomena at the basis of our model.

Released

Propagation of one and two-dimensional discrete waves under finite difference approximation

U. Biccari, A. Marica, E. Zuazua Propagation of one and two/dimensional discrete waves under finite difference approximation,Found Comput Math (2020) ...
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Null controllability of a nonlocal heat equation with an additive integral kernel

U. Biccari, V. Hernández-Santamaría Null controllability of a nonlocal heat equation with an additive integral kernel. SIAM J. Control Optim., ...
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Null-controllability properties of the wave equation with a second order memory term

U. Biccari, S. Micu Null-controllability properties of the wave equation with a second order memory termJ DIFFER EQUATIONS, Vol. 267, ...
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Dynamics and control for multi-agent networked systems: a finite difference approach

U. Biccari, D. Ko, E. Zuazua Dynamics and control for multi-agent networked systems: a finite difference approach. Math. Models Methods ...
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Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential

U. Biccari Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential, Mathematical Control and related fields, DOI: ...
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The Poisson equation from non-local to local

U. Biccari, V. Hernández-Santamaría The Poisson equation from non-local to local, Electronic Journal of Differential Equations, Vol. 2018 (2018), No ...
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Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects

U. Biccari, V. Hernández-Santamaría Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects, IMA J. Math. Control Inf ...
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Local regularity for fractional heat equations

U. Biccari, M. Warna, E. Zuazua Local regularity for fractional heat equations<, Recent Advances in PDEs: Analysis, Numerics and Control, ...
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Local elliptic regularity for the Dirichlet fractional Laplacian

U. Biccari, M. Warna, E. Zuazua Local elliptic regularity for the Dirichlet fractional Laplacian Advanced Nonlinear Studies, Vol. 17, Nr ...
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Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian

U. Biccari, M. Warna, E. Zuazua Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian Adv. Nonlinear Stud., Vol. 17, ...
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Accepted

Null-controllability properties of a fractional wave equation with a memory term

U. Biccari, M. Warna Null-controllability properties of a fractional wave equation with a memory term. Evol. Equ. Control The. Abstract: ...
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Controllability of the one-dimensional fractional heat equation under positivity constraints

U. Biccari, M. Warna, E. Zuazua Internal observability for coupled systems of linear partial differential equations. Commun. Pure Appl. Anal., ...
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Submitted

A stochastic approach to the synchronization of coupled oscillators

Umberto Biccari, Enrique Zuazua. A stochastic approach to the synchronization of coupled oscillators (2020) Abstract. This paper deals with an optimal ...
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Existence and cost of boundary controls for a degenerate/singular parabolic equation

Umberto Biccari, Víctor Hernández-Santamaría, Judith Vancostenoble. Existence and cost of boundary controls for a degenerate/singular parabolic equation (2020). Abstract. In ...
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Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation

Antil H, Biccari U, Ponce R, Warma M, Zamorano S. Controllability properties from the exterior under positivity constraints for a ...
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Model reduction of converter-dominated power systems by Singular Perturbation Theory

U. Biccari, Noboru Sakamoto, Eneko Unamuno, Danel Madariaga, Enrique Zuazua, Jon Andoni Barrena Model reduction of converter-dominated power systems by ...
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Internal control for non-local Schrödinger and wave equations involving the fractional Laplace operator

U. Biccari Internal control for non-local Schrödinger and wave equations involving the fractional Laplace operator Abstract: We analyze the interior ...
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coming soon!

  • 24.06.2019 - 28.06.2019 Course on control problems for non-local PDE , University of Naples
  • 2018/2019. Course on Mathematical Methods For Control Theory, University of Deusto
  • 2017/2018. Course on Mathematical Methods For Control Theory, University of Deusto

Meet our team!