Flow Control in the Presence of Shocks,   Enrique Zuazua,   Bilabo,  Wed, 19 December, 2012,   10:00 a.m. A-233


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 we present an alternate direction method that allows not only dealing with shocks but also taking advantage of their presence to make the optimization processes to converge much master.