Burgers' equation with nonlinear boundary feedback: H-1 stability, well-posedness and simulation

We consider the viscous Burgers' equation under recently proposed nonlinear boundary conditions and show that it guarantees global asymptotic stabiliz ation and semiglobal exponential stabilization in H-1 sense. Our result is global in time and allows arbitrary size of initial data. It strengthens re cent results by Byrnes, Gilliam, and Shubov, Ly, Mease, and Titi, and Ito a nd Yan. The global existence and uniqueness of classical solutions follows from the general theory of quasi-linear parabolic equations. We include a n umerical result which illustrates the performance of the boundary controlle r.