A. Balogh et M. Krstic, Burgers' equation with nonlinear boundary feedback: H-1 stability, well-posedness and simulation, MATH PROB E, 6(2-3), 2000, pp. 189-200
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.