Finite-parameter feedback stabilization of original Burgers' equations and Burgers' equation with nonlocal nonlinearities

We study the problem of global exponential stabilization of original Burgers' equations and the Burgers' equation with nonlocal nonlinearities by controllers depending on finitely many parameters. It is shown that solutions of the controlled equations are steering a concrete solution of the non-controlled system as $t\rightarrow \infty$ with an exponential rate.