Mathematics – Optimization and Control
Scientific paper
2009-02-12
Mathematics
Optimization and Control
22 pages, submitted; v2: misprints corrected, a remark added in section 2
Scientific paper
We study the finite-horizon optimal control problem with quadratic functionals for an established fluid-structure interaction model. The coupled PDE system under investigation comprises a parabolic (the fluid) and a hyperbolic (the solid) dynamics; the coupling occurs at the interface between the regions occupied by the fluid and the solid. We establish several trace regularity results for the fluid component of the system, which are then applied to show well-posedness of the Differential Riccati Equations arising in the optimization problem. This yields the feedback synthesis of the unique optimal control, under a very weak constraint on the observation operator; in particular, the present analysis allows general functionals, such as the integral of the natural energy of the physical system. Furthermore, this work confirms that the theory developed in Acquistapace et al. [Adv. Differential Equations, 2005] -- crucially utilized here -- encompasses widely differing PDE problems, from thermoelastic systems to models of acoustic-structure and, now, fluid-structure interactions.
Bucci Francesca
Lasiecka Irena
No associations
LandOfFree
Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-556358