Nonlinear Neumann boundary stabilization of the wave equation using rotated multipliers.

Pierre Cornilleau (1) , Jean-Pierre Lohéac (1) , Axel Osses (2)

1 ICJ - Institut Camille Jordan
2 USACH - Universidad de Santiago de Chile [Santiago]

We study the boundary stabilization of the wave equation by means of a linear or non-linear 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.

Mots clés: stabilisation; feedback; multiplicateurs

Domaines: Optimisation et contrôle [math.OC]

Pierre Cornilleau, Jean-Pierre Lohéac, Axel Osses. Nonlinear Neumann boundary stabilization of the wave equation using rotated multipliers.. 2007. ⟨hal-00178179v4⟩