Members at UPV/EHU

Profesora Adjunta at UPV/EHU

Jone's page on researchgate

My main research area is the control theory of partial differential equations, specially parabolic or elliptic type equations. I have been working on null control problems with different conditions on the coefficients of the equations and on the domain where we are trying to apply the control. I am also interested in the use of Carleman inequalities, propagation of smallness property and observability inequalities to other research areas.

Profesora Adjunta at UPV/EHU

Naiara's page on the arXiv

My research interests include partial differential equations, relativistic quantum mechanics and spectral theory. In particular, my research is focused mainly on the study of Dirac Hamiltonians with critical singularities, self-adjoint extensions, spectral properties, Shell interactions, confinement and hadron bag models.

Profesor Adjunto at UPV/EHU 

Jon's webpage

My main research area is Control Theory. In particular, my research focusses on controlling parabolic and dispersive equations, as well as neural ordinary differential equations. I am also interested in the existence and uniqueness of solutions of partial differential equations and on their asymptotic properties.

IKERBASQUE Research Professor at UPV/EHU and at BCAM

Jean-Bernard's home page at BCAM and at IKERBASQUE.

J.-B. Bru is an Ikerbasque Research Professor at both the mathematics department of the University of the Basque Country (UPV/EHU) and at the Basque Center for Applied Mathematics (BCAM). He started his career as an independent researcher in 1999 with a PhD in mathematical physics from the University of Aix-Marseille II (France). Before settling in the Spanish Basque country in 2009, he has been in several places from 1999, like the mathematics department of the University of California at Davis (USA), the School of Theoretical Physics (D.I.A.S.) in Dublin (Ireland), the mathematics department of Johannes Gutenberg-University Mainz (Germany), and the Physics University of Vienna (Austria). The bulk of his research covers a scope from mathematical analyzes of the many-body problem to operator algebras, stochastic processes, differential equations, convex and functional analysis.

Profesor interino at UPV/EHU

Javier's website

My research focuses on geometric aspects of Harmonic Analysis, more precisely, using geometric techniques to obtain weighted inequalities for singular integral operators.

IKERBASQUE Research Fellow and Ramon y Cajal fellow at UPV/EHU 

Lucrezia’s homepage

My research is concerned both with the investigation of characterizing features connected with dispersive partial differential equations and the mathematical rigorous study of spectral properties of self-adjoint and non-self-adjoint Hamiltonians of quantum mechanics. My most recent research interests include spectral theory, uncertainty principles and unique continuation, dispersive and Strichartz estimates for wave-type problems and Maxwell systems and Hardy-Rellich type inequalities.

Associate Research Professor (Personal Doctor Investigador Permanente) at UPV/EHU 

Carlota's home page.

My research interest is in nonlinear evolution partial differential equations. In particular, the study of front propagation phenomena in equations of pseudo-parabolic, kinetic, parabolic and hyperbolic type. This amounts to study travelling waves and rarefaction waves, moving interfaces and fronts invading unstable states.

Some of my research on the above topics was motivated by physical problems arising in infiltration in porous media. Most recently, I have looked at some fluid dynamic problems related to this issue from a more applied, although still mathematical, point of view. This includes modelling and rigorous mathematical analysis of accumulation in thin-film viscous flows over a smooth substrate in a limit in which both gravity and surface tension balance. Currently, I am also interested in understanding some processes of two-phase flow at the pore scale in order to derive models of two-phase porous media flows.

PhD student at UPV/EHU

Xuban's page on researchgate

The main topic of my thesis is "Nonlocal regularisations of nonlinear conservation laws". Regarding the nonlinearity of the conservation law, we are considering two cases the first one with a genuinely nonlinear flux function, in which the equation is regularised by a fractional Caputo derivative in space, and the second one is with a non-genuinely nonlinear flux function, in which a dispersion term also is needed apart from the Caputo derivative. These equations are called the nonlocal generalised Burgers equation and the nonlocal generalised Korteweg-de Vries-Burgers equation. Therefore, we are studying different properties of certain class of solutions which are called entropy solutions: existence, uniqueness, vanishing viscosity limits, travelling wave solutions etc.

Profesor Catedrático at UPV/EHU

Miguel's website

I work on linear and nonlinear PDE's and kinetic equations. I am interested in particular in their qualitative properties like long time behavior and singularity formation.

IKERBASQUE Research Professor at UPV/EHU and at BCAM

Luca's webpage at Ikerbasque

I’ve previously been Associate Professor at Rome “Sapienza” University. My research topic is mainly concerned with Dispersive PDE’s and Spectral Theory. I’m mostly interested in the link between Harmonic Analysis, spectral properties and related space-time asymptotic of the main dispersive propagators (Schródinger, Wave, Klein-Gordon, Dirac). One of the main targets of my research is now to understand the role of zero-modes and resonances along nonlinear dynamics, and how they do appear in the linearized spectra.

In my recent career as a professor, I supervised 23 bachelor students, 18 master thesis ("trabajos finales de master”), 2 Ph.D. thesis and 1 post-doc student. I’ve been finalist at the 2014 ERC Starting Grant Call, “Rendiconti Prize” in 2008 and three times “Teaching Prize” at the Science Faculty of Rome Sapienza.

Profesor Adjunto at UPV/EHU

Aingeru's website

My field of interest lays on unique continuation properties for partial differential equations. In my thesis, finished in 2015, I gave an analogous version of Hardy's Uncertainty Principle in the discrete setting, that can be rewritten in terms of unique continuation properties for solutions of the discrete Schrödinger equation.

Profesor Adjunto at UPV/EHU

Andoni's page on researchgate

I’ve been previously been Juan de la Cierva postdoc fellow at BCAM, and lecturer at Faculty of Engineering at Mondragon Unibertsitatea.

I work on inverse problems arising in PDEs. My interest goes from problems of regularity to transmission eigenvalues and inverse scattering. Recently, I have also got interested in problems where there is a specific uncertainty which is modelled by random fields.

IKERBASQUE Research Associate at UPV/EHU

Mihalis's page on researchgate

My research lies at the interface of (non-homogeneous) Harmonic Analysis, Elliptic Partial Differential Equations and Geometric Measure Theory. The last few years, I had focused on the connection of the analytic properties of classic PDE objects in domains with rough boundaries with the geometric properties of the domain and its boundary. Although, I am interested in many different types of problems related to those fields.

IKERBASQUE Research Associate at UPV/EHU

Ioannis's website

I'm working on harmonic analysis, directional singular integrals, time-frequency analysis, operator theory, and weighted norm inequalities.

IKERBASQUE research professor at UPV/EHU and at BCAM

Carlos's website at BCAM and at Ikerbasque

Carlos is an Ikerbasque Research Professor at both the mathematics department of the University of the Basque Country (UPV/EHU) and at the Basque Center for Applied Mathematics (BCAM). 

He obtained his PhD in Washington University, S. Louis (1989).  He enjoyed a postdoctoral position at Brock University (Canada) and several visiting positions at USA. Then he became associate Prof. at the Autonomous University of Madrid 1992-2001 and then he obtained a full professorship at the University of Seville in 2000. In 2014 he was appointed  Ikerbasque Research Professor at the Department of Mathematics of the University of the Basque Country. Since September of 2015 he became a member of BCAM as guarantor of the Severo Ochoa's grant enjoyed by BCAM.

His research is mainly focused in the area of Real and Harmonic Analysis: singular integrals, weighted norm inequalities, commutators of singular integrals,  multilinear and multiparameter aspects of Harmonic Analysis. He also works at the interface between Harmonic Analysis and Elliptic Partial Differential Equations like degenerate Poincaré-Sobolev. 

Professor Catedrático at UPV/EHU

Luis's page at UPV/EHU

My research is mainly focused in the interplay of Fourier Analysis and Partial Differential Equations of Mathematical Physics. More recently I have been interested in the deep connection between uncertainty principles, that are easily described using the Fourier transform, and lower bounds for solutions of linear and non-linear dispersive equations. A consequence of these estimates from below is that compact perturbations of a solitary wave or soliton instantaneously destroys its exponential decay. Another one of my recent interests is on fluid mechanics and turbulence. More concretely in the so called Localized Induction Approximation for the evolution of vortex filaments and the relevance of the presence of corners in the filament. The results concerning regular polygons seem to me quite striking. Finally, I have been also working on relativistic and non-relativistic equations with singular electromagnetic potentials. The singularities of the potentials are critical from the point of view of the scaling symmetry.