Coloquio del IMUNAM - C. U. febrero 2025

In this talk, we discuss the exponential stabilization of the one-dimensional heat equation when the feedback control is acting through the boundary. We begin by introducing the concept of stabilization with a simple example from ODEs. Then we explain the Backstepping method for heat equation with its importance and drawbacks. Finally, we show how this approach can also be useful to stabilize more complicated systems, such as linearized compressible Navier-Stokes and FitzHugh-Nagumo-type systems (nonlinear). This talk is based on one-variable Sobolev spaces, classical energy estimates of PDEs and certain integral equations.