The general problem of this paper is the analysis of wave propagation in a bounded medium where the uncontrolled boundary obeys a coupled differential equation. More precisely, we study a one-dimensional wave equation with a nonlinear second-order dynamic boundary condition and a Neuman-type boundary control acting on the other extremity. A generic class of nonlinear collocated feedback laws is considered. Hadamard well-posedness is established for the closed-loop system, with initial data lying in the natural energy space of the problem. Moreover, we investigate an example of stabilization through a proportional controller. t 0 g(s) ds for a.e. t in (0, T). Such class f is identified with its continuous

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.