A direct method for the boundary stabilization of the wave equation 论文

摘要

We consider the wave equation y''−Δy=0 in a bounded domain Ω⊂R n with smooth boundary Γ, subject to mixed boundary conditions y=0 on Γ 1 and δy/δv=F(x,y') on Γ 0 , (Γ 0 ,Γ 1 ) being a partition of Γ. We study the boundary stabilizability of the solutions i.e. the existence of a partition (Γ 0 ,Γ 1 ) and of a boundary feed-back F (.,.) such that every solution decays exponentially in the energy space as t tends to infinity. We prove the stabilizability of the system without geometrical hypothesis on Ω (at least if n≤3). This method is rather general and can be adapted to other evolution system (e.g. models of plates, elasticity systems) as well