## Mathematics Colloquium

Date: Time: 4:00 pm–4:50 pmAffiliation: Iowa State

Local Host: Daniel Toundykov

Title: Moment Method in Control Theory of Systems of PDEs

Additional Public Info:

Abstract: A control problem for a differential equation seeks a control function u

such that the solution y to Cauchy problem y’(t) = f(t,y(t),u(t)), y(0) = y_0, reaches a certain prescribed value at time T. One of several approaches that can sometimes be applied to analyze controllability problems involving

systems of coupled partial differential equations is the moment method. In

this approach, the control problem is reduced to a system of moment containing

coefficients {c_k} given in a linear space that is determined by the space of initial data, terminal data and control parameters. Here I is a time interval, {p_k} is a given sequence of independent functions on I, and u is the control function that is to be determined. Usually,

the p_k are exponentials of the form $exp(lambda_k t), where lambda_k is a system eigenvalue. I’ll describe a variety of results that can be obtained by the moment method and how the geometry of the eigenvalues influences the type of solution one obtains.

Refreshments will be served in 348 Avery 3:30-4pm.

The talk is free and open to the public.