Abstract
Flow control is one of the most challenging and relevant topics connecting the theory of Partial Differential Equations (PDE) and Control Theory. On one hand the number of possible applications is huge including optimal shape design in aeronautics. On the other hand, from a purely mathematical point of view it involves sophisticated models such as Navier-Stokes and Euler equations, hyperbolic systems of conservations laws, that constitute, certainly, one of the main challenges of the theory of PDE. Indeed, some of the main issues concerning existence, uniqueness and regularity of solutions are still open in this field. Moreover, Control Theory also faces some added difficulties when addressing these issues since the possible presence of singularities on solutions makes often classical approaches fail.
In this lecture the speaker presents joint work in collaboration with Prof Carlos Castro from Universidad Politécnica de Madrid, and Dr Francisco Palacios from Stanford University, in which they propose a new alternating direction method that allows not only dealing with shocks but also taking advantage of their presence to make the optimization processes to converge much faster.
About the speaker
Prof Enrique Zuazua received his PhD in Mathematics from Universidad del País Vasco-Euskal Herriko Unibertsitatea in 1987 and Université Pierre et Marie Curie in 1988. He has joined the faculty of Universidad Autónoma de Madrid since 1988. He is currently the founding Scientific Director of Basque Center for Applied Mathematics (BCAM), Director of the BCAM Chair in PDE, Control and Numerics and also Research Professor at Ikerbasque, Basque Foundation for Science.
Prof Zuazua’s fields of specialization cover PDE, systems control and numerical analysis. These interconnected fields have as ultimate goal the modeling, analysis, computer simulation and control and design of natural phenomena and other problems arising in research and development. He was recognized as a "highly cited researcher" by the ISI Institute in 2004.
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