  This paper presents a novel methodology for the design of boundary feedback
stabilizers for 1-D, semilinear, parabolic PDEs. The methodology is based on
the use of small-gain arguments and can be applied to parabolic PDEs with
nonlinearities that satisfy a linear growth condition. The nonlinearities may
contain nonlocal terms. Two different types of boundary feedback stabilizers
are constructed: a linear static boundary feedback and a nonlinear dynamic
boundary feedback. It is also shown that there are fundamental limitations for
feedback design in the parabolic case: arbitrary gain assignment is not
possible by means of boundary feedback. An example with a nonlocal nonlinear
term illustrates the applicability of the proposed methodology.
