National Physical Laboratory

Flow control in the presence of shocks

Further Information

Recorded: 3 November 2011

Speakers: Enrique Zuazua

Related: Mathematics and Scientific Computing

Flow control in the presence of shocks

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 often makes classical approaches fail.

In this lecture we present recent joint work in collaboration with Carlos Castro and Francisco Palacios in which we propose a new alternate direction method that allows not only dealing with shocks but also taking advantage of their presence to make the optimization processes converge much faster.

Last Updated: 3 May 2012
Created: 4 Nov 2011