Controllability and Observability Theory of Certain Parabolic Integrodifferential Equations

The exact null controllability of linear and nonlinear parabolic integrodifferential equations with space-periodic boundary conditions are studied. Carleman estimate for the linearized problem providing the observability results is fundamental to the analysis and by duality also provides exact global controllability. Local exact controllability for the nonlinear problem is obtained using the Kakutani fixed-point theorem.