Nonlinear neumann boundary stabilization of the wave equation using rotated multipliers

Abstract

We study the boundary stabilization of the wave equation by means of a linear or nonlinear Neumann feedback. The rotated multiplier method leads to new geometrical cases concerning the active part of the boundary where the feedback is applied. Due to mixed boundary conditions, these cases generate singularities. Under a simple geometrical condition concerning the orientation of the boundary, we obtain stabilization results in both cases.