  This paper deals with a one-dimensional wave equation with a nonlinear
dynamic boundary condition and a Neumann-type boundary control acting on the
other extremity. We consider a class of nonlinear stabilizing feedbacks that
only depend on the velocity at the controlled extremity. The uncontrolled
boundary is subject to a nonlinear first-order term, which may represent
nonlinear boundary anti-damping. Initial data is taken in the optimal energy
space associated with the problem. Exponential decay of the mechanical energy
is investigated in different cases. Stability and attractivity of suitable
invariant sets are established.
