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.
Books
B. Lee and L. Markus, Foundations of Optimal Control Theory, John Wiley, 1968.
L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer, 1991.
L. 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 Delhi, 1989.
Dal Maso, An Introduction to $\Gamma$-Convergence, Birkhauser, 1993.