Theoretical and Numerical Analysis of Evolution Equations
Objective:The current project focuses on several mathematical aspects of the evolution of physical systems that can be modeled by partial differential equations and whose applicability ranges from quantum physics to fluid dynamics. An essential part of the current proposal considers theoretical questions related to uniqueness and inverse problems. A main tool that we use extensively are the Carleman estimates. The application of these techniques to prove uncertainty principles, which is 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 scratched the surface 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 the Dirac and Schrödinger equations, both in the linear and in the non-linear settings. We will look at some spectral problems related to these equations. Also some applications will be considered such 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 and the study of toy models of porous media flows that shall mimic some hysteresis phenomena characteristic of these flows. Analysis of partial differential equations with fractional diffusion and its role in combination with dispersive terms, as well as the study of some special solutions of nonlinear dispersive equations will also be subject to 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. Some are as classical as the successful treatment of absorption of energy at the boundary of a truncated domain for the wave equation, issue that can be addressed from the point of view of inverse problems. Other questions concern the adequacy of spectral and pseudo-spectral methods for the simulation of hyperbolic systems of nonlinear partial differential equations, being the shallow water equations over a sphere a practical example.
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