Bifurcations and attractors for a boundary feedback controlled Burgers equation

In this work we consider an open loop system consisting of a viscous Burgers' equation with or without an additional forcing. Control inputs and outputs are introduced through the boundary and a closed loop system is obtained by introducing a proportional error boundary feedback law. The main point of the talk is to present several known results for this system and draw attention to some open problems. Topics discussed in the talk will include global existence and regularity of solutions, existence of local and global attractor, semiglobal and practical stabilization, and bifurcation of dynamics associated with variation of the gains in the boundary feedback law.