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.
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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 current research interests cover numerous areas of PDE analysis and control, including:

  • different classes of non-local models such as hyperbolic, parabolic and dispersive fractional PDE, memory-type equations or PDE with integral potentials;
  • numerical analysis for local and non-local PDE with control purposes;
  • controllability properties of PDE with singular inverse-square potentials and/or variable degenerate coefficients;
  • analysis and control of collecting behavior models and their micro-macro limit;
  • stochastic methods applied to control problems

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

See complete CV

  • 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.

Certifications

  • IKERTRAMOS call 2019: positive evaluation of the Agencia de Calidad del Sistema Universitario Vasco (UNIBASQ) for the research activity in the 6 years period 2013-2018
  • AYUDANTE DOCTOR: positive evaluation of the Agencia Nacional de Evaluación de la Calidad y Acreditación (ANECA) for the role of assistant professor

Released

Control and Numerical approximation of Fractional Diffusion Equations

Umberto Biccari, Mahamadi Warma, Enrique Zuazua. Control and Numerical approximation of Fractional Diffusion Equations (2022) Handb. Numer. Anal. Elsevier. ISSN:1570-8659, DOI: ...
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A stochastic approach to the synchronization of coupled oscillators

Umberto Biccari, Enrique Zuazua. A stochastic approach to the synchronization of coupled oscillators. Frontiers in Energy Research, section Smart Grids. Front ...
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Controllability of the one-dimensional fractional heat equation under positivity constraints

U. Biccari, M. Warma, E. Zuazua. Controllability of the one-dimensional fractional heat equation under positivity constraints Commun. Pure Appl. Anal., ...
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Null-controllability properties of a fractional wave equation with a memory term

U. Biccari, M. Warma Null-controllability properties of a fractional wave equation with a memory term. Evol. Eq. Control The., Vol ...
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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., ...
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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, Math. Control Relat. F., Vol. 9, ...
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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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Accepted

Internal control for a non-local Schrödinger equation involving the fractional Laplace operator

U. Biccari Internal control for a non-local Schrödinger equation involving the fractional Laplace operator (2021) Abstract: We analyze the interior ...
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Submitted

A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation

U. Biccari, Y. Song, X. Yuan, E. Zuazua. A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a ...
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Multilevel selective harmonic modulation by duality

Biccari U, Zuazua E. Multilevel selective harmonic modulation by duality (2021) Abstract. We address the Selective Harmonic Modulation (SHM) problem ...
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Multilevel control by duality

Umberto Biccari, Enrique Zuazua. Multilevel control by duality (2021) Abstract. We discuss the multilevel control problem for linear dynamical systems, consisting ...
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Optimal control of linear non-local parabolic problems with an integral kernel

Umberto Biccari, Víctor Hernández-Santamaría, Loic Louison, Abdennebi Omrane. Optimal control of linear non-local parabolic problems with an integral kernel. (2021) Abstract ...
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Blow-up results for a logarithmic pseudo-parabolic p(.)-Laplacian type equation

Abita Rahmoune, Umberto Biccari. Blow-up results for a logarithmic pseudo-parabolic p(.)-Laplacian equation. (2021) Abstract. In this paper, we consider an initial-boundary ...
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Multiplicity of solutions for fractional q(.)-Laplacian equations

Abita Rahmoune, Umberto Biccari. Multiplicity of solutions for fractional q(.)-Laplacian equations. (2021) Abstract. In this paper, we deal with the following ...
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Multilevel Selective Harmonic Modulation via Optimal Control

Deyviss Jesús Oroya-Villalta, Carlos Esteve-Yagüe Umberto Biccari. Multilevel Selective Harmonic Modulation via Optimal Control. (2021) Abstract. We consider the Selective Harmonic ...
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Stochastic optimization methods for the simultaneous control of parameter-dependent systems

Umberto Biccari, Ana Navarro-Quiles, Enrique Zuazua. Stochastic optimization methods for the simultaneous control of parameter-dependent systems (2020) Abstract. We address the ...
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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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Academic courses

  • 01.09.2019 - 31.01.2022 Algebra, Bachelor degree in Computer Engineering, (6 ECTS), University of Deusto, Bilbao campus, Spain
  • 01.09.2020 - 31.01.2021 Mathematics, Bachelor degree in Business Administration (6 ECTS), University of Deusto, San Sebastián campus, Spain
  • 01.09.2019 - 31.01.2020 Mathematics, Bachelor degree in Business Administration (6 ECTS), University of Deusto, San Sebastián campus, Spain

Other courses

  • 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!