In this paper, we propose a fortified boundary control law and an adaptation law for Burgers' equation with unknown viscosity, where no a priori knowledge of a lower bound on viscosity is needed. This control law is decentralized, i.e., implementable without the need for central computer and wiring. Using the Lyapunov method, we prove that the closed-loop system, including the parameter estimator as a dynamic component, is globally H 1 stable and well posed. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's Lemma which can not be used in the present situation. Key Words: Burgers' equation; Adaptive control; Boundary control; Lyapunov design. To appear in International Journal of Adaptive Control and Signal Processing # This work was supported by O#ce of Naval Research, Air Force O#ce of Scientific Research, National Science Foundation and Killam Trust. + This work was performed while the author was a postdoc at UC San ..