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SHORT COURSE: PDE Control and Numerics

Start Date: October 20, 2015 9:00 AM
End Date: October 21, 2015 12:00 PM

Professor Enrique Zuazua

Universidad Autónoma de Madrid, Spain

Abstract: In this series of lectures we shall discuss several topics related with the modelling, analysis, numerical simulation and control of Partial Differential Equations (PDE) arising in various contexts of Science and Technology In these lectures we shall introduce some of the most relevant work that has been done in the subject in recent years, paying special attention to the fundamental methodological aspects, and pointing towards some potential future perspectives of research. After a short introduction to the finite-dimensional theory, we shall then describe the basic theory for the wave and heat equation, to later address some important multi-physics models Then we shall address the problem of the numerical approximation of control problems. To begin with we shall show that the control and the numerical approximation process do not commute so that, in general, when controlling a finite-dimensional approximation of the continuous model, one does not actually compute an approximation of the control one is looking for. We shall see what are the possible remedies to these pathologies: space discretizations, numerical damping, filtering of high frequencies, multi-grid algorithms, etc.The latter fact is of great impact from a modelling point view since in practical applications numerical approximation schemes may also be used (and they are often used that way) as discrete models. To conclude, we shall present a list of open problems and directions of possible future research.

Bio: Enrique Zuazua is professor at  Departamento de Matemáticas Universidad Autónoma de Madrid in Spain. He obtained his  PhD at the Université Pierre et Marie Curie (UPMC) in Paris, with financial support of the Basque Government, at the present “Laboratoire Jacques Louis Lions”, at that time, the “Laboratoire d’Analyse Numérique.”  He received a dual PhD diploma from UPV/EHU in 1987 and the UMPC in 1988. Since then he  has been a Professor of Applied Mathematics in Universidad Complutense de Madrid (1990-2001) andUniversidad Autónoma de Madrid (2001-2008). More recently, since September 2008, he has been an IkerbasqueResearch Professor in Bilbao, where he had the honor of being the Founding Scientific Director of BCAM – Basque Center for Applied Mathematics. In September 2014  he was promoted to Distinguished Ikerbasque Professor. Since September 2015 he is back to his position at UAM in the Cantoblanco Campus in Madrid. His areas of research  in Applied Mathematics include Partial Differential Equations, Control Theory and Numerical Analysis. These subjects interrelate with the aim of modeling, analyzing and simulating a variety of natural phenomena and industrial processes, with the final goal of contributing to their control and design. 

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