# Optimization and optimal control forparabolic and hyperbolic equations:Fourier method and someregularization techniques

## Nadir Bayramov

**Feb. 7, 2012, 2:30 p.m. S2 046**

The talk is devoted to the general Fourier method for solution of optimal control problems used in my Master Thesis and in some previous research work while studying at Moscow State University. Parabolic equation as a model of air pollution of the environment, and hyperbolic equation, describing vibrations of a membrane or a plate, are considered as well as control problems (with quadratic cost functionals) for them, where control is found in the state equation. Common approach using expansion of state and control into Fourier series is described, as well as arising problems with generalization of results for various types of control, domain of the system, boundary conditions and the minimized cost functional.