The program subject of this Doc-Course is "Partial Differential Equations: Analysis, Numerics and Control". The main goal of this program is to provide basic training on advanced mathematical tools for modelling and analysis of systems that arise in applied sciences by means of Partial Differential Equations (PDEs).
The relevance of mathematical analysis to understand and improve the behavior of real systems using PDEs is steadily increasing in the last years. This relevance is enhanced by the development of sientific computing, that makes possible not only to analyze, describe and predict the behavior of the systems, but also to optimize it.
We are interested in systems which appear in physics, biology, chemistry, engenieering, ... Mathematics provide deep insight in three main applications: to provide qualitative understanding, quantitative simulation and to optimize the behavior of these systems. We intend to cover these three aspects in this program.
Within this perspective, this program furnishes basic research training in optimization, qualitative analysis and numerical simulation, understood as the main tools for mathematical analysis of systems. It is structured in four Research Units (click on the links to expand the information):
Each Research Unit is composed of a course, individual research projects and several conferences. The course is intended to provide the basic aspects of the subject with a large perspective. The research project focuses on up-to-date subjects, is developed individually and advised by a specific senior reseacher. The conferences are taught by high-level reseachers, and deal with emerging subjects related to each Research Unit.