Differential Equations and Dynamics Seminar

Speaker: Nick Pavel, Ohio University, department of Mathematics.

Title: Optimization and some Optimal Control problems  for differential equations with periodic boundary conditions.

Abstract: We will start with some constrained extrema in finite dimensional spaces,  in some "critical cases" in which
the extrema exist but there are no Lagrange Multipliers. Then we discuss some  "critical cases " (in infinite dimensional
Banach spaces) in which  the "Hessian" (i.e. the second Frechet derivative) is not strictly positive definite.  Finally, we
discuss the regularity of the optimal pair  (y,u)  of a control problem of some simple differential equation with periodic
boundeary conditions. Open problems are pointed out.