CONTROL AND HOMOGENIZATION
Prerequisites: Sobolev spaces,
Elliptic boundary value problems, Heat and wave equations, Variational
formulation and semigroup theory.
Optimal Control of PDE: Optimal control
problems governed by elliptic equations and linear parabolic and hyperbolic
equations with distributed and boundary controls, Computational methods.
Homogenization: Examples of periodic
composites and layered materials. Various methods of homogenization.
Applications and Extensions: Control in
coefficients of elliptic equations, Controllability and Stabilization of
Infinite Dimensional Systems, Hamilton-Jacobi-Bellman equations and Riccati
equations, Optimal control and stabilization of flow related models.
Lee and L. Markus, Foundations of Optimal Control Theory, John Wiley, 1968.
Lions, Optimal Control of Systems Governed by Partial Differential Equations,
Lions, Controlabilite exact et Stabilisation des systemes distribues, Vol. 1,
2 Masson, Paris 1988.
Bardi, I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of
Hamilton-Jacobi-Bellman Equations, Birkhauser, 1997.
Kesavan, Topics in Functional Analysis and Applications, Wiley-Eastern, New
Maso, An Introduction to $\Gamma$-Convergence, Birkhauser, 1993.