  This paper provides global exponential stabilization results by means of
boundary feedback control for 1-D nonlinear unstable reaction-diffusion Partial
Differential Equations (PDEs) with nonlinearities of superlinear growth. The
class of systems studied are parabolic PDEs with nonlinear reaction terms that
provide "damping" when the norm of the state is large (the class includes
reaction-diffusion PDEs with polynomial nonlinearities). The case of Dirichlet
actuation at one end of the domain is considered and a Control-Lypunov
Functional construction is applied in conjunction with Stampacchia's truncation
method. The paper also provides several important auxiliary results; among
which is an extension of Wirtinger's inequality, used here for the construction
of the Control Lyapunov functional.
