Umberto Biccari

Associated 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.
Check my Publons \| ORCID \| Google Scholar

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

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 ...

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: ...

Multilevel control by duality

Umberto Biccari, Enrique Zuazua. Multilevel control by duality (2023) Systems & Control Letters, Vol. 175, 105-502, https://doi.org/10.1016/j.sysconle.2023.105502 Abstract. We discuss the ...

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 (2022), Vol. 11, No. 1: 301-324 ...

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 ...

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., ...

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 ...

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 (2022). Mathematical Control ...

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., ...

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., ...

<!--

Accepted

Control of neural transport for normalizing flows

D. Ruiz-Balet, E. Zuazua. Control of neural transport for normalizing flows (2023) J. Math. Pures Appl. https://doi.org/10.48550/arXiv.2307.07817 Abstract. Inspired by ...

Multilevel Selective Harmonic Modulation via Optimal Control

Umberto Biccari, Carlos Esteve-Yagüe, Deyviss Jesús Oroya-Villalta. Multilevel Selective Harmonic Modulation via Optimal Control. (2022) Applied Mathematics and Optimization Abstract. We ...

-->

20.06.2022 FAU DCN-AvH Mini workshop: Recent advances: (Multilevel Control), FAU - Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany PDF Slides
31.01.2020 Controllability of Fractional Heat Equations under Positivity Constraints, 5th. Congress of young researchers RSME, Castelló, Spain, PDF Slides
21.08.2019 Controllability of the 1d fractional heat equation under positivity constraints, 8th workshop on Partial Differential Equations, optimal design and numerics, Benasque, Spain | PDF Slides
03.04.2019 Dynamics and control for multi-agent networked systems, Universidad de Cantabria, Santander, Spain | PDF Slides
14.03.2019 Dynamics and control for multi-agent networked systems, Friedrich-Alexander Universität, FAU Erlangen-Nürnberg, Germany | PDF Slides
05.12.2018 Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects, 1st workshop on dynamics, control and numerics for fractional PDE’s, San Juan, Puerto Rico | PDF Slides
30.08.2018 Propagation of one and two-dimensional discrete waves under finite difference approximation, 14th French-Romanian conference in applied mathematics, Bordeaux, France | PDF Slides
06.07.2018 Propagation of one and two-dimensional discrete waves under finite difference approximation, University of Craiova, Romania | PDF Slides
01.03.2018 Controllability of Partial Differential Equations with integral kernels, MINAKE 2018 – Microlocal and Numerical Analysis, Kinetic Equations Control Conference, Madrid, Spain | PDF Slides
29.08.2017 Finite Element approximation of the one-dimensional fractional Poisson equation with applications to numerical control, 7th workshop on Partial Differential Equations, optimal design and numerics, Benasque, Spain | PDF Slides
25.08.2017 Control of partial differential equations involving the fractional Laplacian, 7th workshop on Partial Differential Equations, optimal design and numerics, Benasque, Spain, PDF Slides
08.03.2017 Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function, Universidad Autónoma de Madrid, Spain.

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

Associated Researcher

Released

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

Control and Numerical approximation of Fractional Diffusion Equations

Multilevel control by duality

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

A stochastic approach to the synchronization of coupled oscillators

Controllability of the one-dimensional fractional heat equation under positivity constraints

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

Existence and cost of boundary controls for a degenerate/singular parabolic equation

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

Null controllability of a nonlocal heat equation with an additive integral kernel

Accepted

Control of neural transport for normalizing flows

Multilevel Selective Harmonic Modulation via Optimal Control

Submitted

Gaussian Beam ansatz for finite difference wave equations

Controllability and Positivity Constraints in Population Dynamics with age, size Structuring and Diffusion

Null Controllability for a Degenerate Structured Population Model

Optimal control of linear non-local parabolic problems with an integral kernel

Blow-up results for a logarithmic pseudo-parabolic p(.)-Laplacian type equation

Multiplicity of solutions for fractional q(.)-Laplacian equations

Stochastic optimization methods for the simultaneous control of parameter-dependent systems

Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation

Model reduction of converter-dominated power systems by Singular Perturbation Theory

Meet our team!