42,930 research outputs found
Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions
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.Comment: 22 pages, submitted; v2: misprints corrected, a remark added in
section
Ergodic Mean Field Games with H\"ormander diffusions
We prove existence of solutions for a class of systems of subelliptic PDEs
arising from Mean Field Game systems with H\"ormander diffusion. These results
are motivated by the feedback synthesis Mean Field Game solutions and the Nash
equilibria of a large class of -player differential games
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