Parabolic and Hyperbolic partial differential equations, Concept of controllability (Exact controllability, Approximate controllability, Null controllability, Trajectory controllability etc.) for Finite dimensional control system as well as for the Infinite dimensional control Systems governed by the Heat equations and Wave equations. Semigroups of linear operators and its application to the Heat and Wave equations, Observability and controllability, Stabilizability, Carleman estimate for the Heat Operator, Null Controllability for the Heat equations, Boundary control system, Numerical method for steering controls in the controllability problems.
