Mathematical and numerical analysis of some partial differential equations and their applications
Objective:The current project focuses on several mathematical aspects of physical systems that can be modeled by partial differential equations and which applicability ranges from quantum physics to fluid dynamics and economy. An essential part of the current proposal considers theoretical questions related to uniquene continuation and control in different parabolic and elliptic equations. A main tool that we use extensively use are Carleman estimates. The application of these techniques to prove uncertainty principles, which one of the classical questions in Fourier Analysis, has been a breakthrough obtained by our group in recent years. Our impression is that we have just seen the tip of the iceberg and thus we propose to go as deep as possible into the subject. A second part is concerned with the study of evolution problems. In particular, we will study some fundamental equations of Mathematical Physics such as Dirac and Schrödinger equations both in the linear and the non-linear setting. We will look at some spectral problems related to these equations. We will study Oscillatory Integrals and Fourier Integral Operators (FIO) and its connection with some classical maximal functions and its application in the regularity of some PDEs. Also some applications will be considered, as, for example, the evolution of vortex filaments and its connection with turbulence and the possibility of confinement for relativistic particles. Other problems, concern the study of viscous flows, such as the existence of some relevant self-similar solutions of the thin-film equation, in particular those that describe lifting and rupture of the film. Analysis of PDEs with fractional diffusion of porous medium type and the role of non local diffusion terms in combination with dispersive terms will also be subject of study. In many of the problems already mentioned, numerical computations represent a complementary technique that is useful in the analysis of the underlying properties of solutions. However, we are also interested in some theoretical questions of numerical analysis such as spectral and pseudo-spectral methods for PDEs posed in unbounded domains.
MATH4SPORTS - Modelización matemática para la industria deportiva: salud y rendimiento
MATH4SPORTS seeks to transfer applied mathematics as a driving technology to the field of the sports industry, with a high potential for technology transfer to start-ups, professional clubs, researchers and other agents in the innovative environment of Bizkaia.
M-KONTAK - Investigación de los Fenómenos Asociados al Contacto Metal-Metal en Tecnologías de H2 a Alta Presión
The main objective of the M-KONTAK project is to gain an in-depth understanding of the failure modes and their effect on metallic materials and the surfaces of threaded joints in candidate technologies for high-pressure H2 effect on the metallic materials and surfaces that make up the threaded jo
KAIROS - Digitalización predictiva del comportamiento a largo plazo de materiales poliméricos composites. Empleo de IA, modelización basada en la física y metodologías de aceleración de ensayos
KAIROS was created with the main objective of researching and obtaining a solution that allows multi-scale digitisation combined with ML and accelerated testing methodologies, for the study of the long-term behaviour (creep, fatigue, ageing) of polymeric materials applicable, for example, to the
CHARGER+ - Nueva Generación de Puntos de Recarga de Vehículo Eléctrico con Funcionalidades Autónomas y Colaborativas e Impacto Cero
The general objective of the CHARGER+ project is to generate the necessary knowledge to define a new generation of electric vehicle (EV) charging points, so that the related Basque companies (electricity companies, charging post installation companies and charger manufacturers) will be in an adva