Explore the asymptotic analysis and null controllability of the advection-diffusion equation in this 50-minute lecture from the Hausdorff Trimester Program on Kinetic Theory. Delve into the solution behavior of yt − εyxx + yx = 0 as the parameter ε approaches zero. Examine the intricate interactions between boundary and internal layers. Investigate the null controllability properties of the equation in the limit as ε tends to zero. Gain insights into advanced mathematical techniques for analyzing partial differential equations and their asymptotic behavior.