On energy wave equations with non-negative non-linear terms

• Results on existences of global solutions.
• Special conditions where there is uniqueness of solutions.
• One rate of uniform stability for the energy.

This paper deals with the existence of at least one solution and the uniform stabilization of the energy of an initial-boundary value problem for a non-linear wave equation with non-linear boundary condition of the feedback type. The non-linearities in both waves and boundary equations behave as functions of the type |u|Rϱ for ϱ>1ϱ>1.