中科院数学与系统科学研究院

华罗庚数学研究中心

学术报告

报告人：Prof. Frederic Marbach (University of Rennes, France)

题  目：Controllability despite boundary layers

时  间：2018.05.03, 15:00-17:00

地  点：N913室

摘  要：Controllability is the question of whether one can find a source-term (the control) to drive the solution of an evolution equation from a given initial state to a prescribed final state. In this lecture, we will study the question of controllability in small time for systems coming from fluid mechanics (Burgers, Navier-Stokes). I will explain why answering this question implies understanding the behavior of boundary layers. Several usual techniques will be used: asymptotic expansions, Coron's return method, energy estimates (Sobolev or analytic). I will also explain a recent technique to build controls that enhance the dissipation of the involved boundary layers.