We consider the wave equation dampedwith a boundary nonlinear velocity feedback p(u'). Under some geometrical conditions, we prove that the energy of the system decays to zero with an explicit decay rate estimateeven if the function ρ has not a polynomial behavior in zero.This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction of a special weight function(that depends on the behavior of the function ρ in zero), and on a new nonlinear integral inequality.
