The Stabilization of a Linearized Self-Excited Wave Equation by an Energy Absorbing Boundary

• Main Authors: Sarhangi, G.R., Najafi, M., Wang, H.
• Format: Conference Proceeding
• Language: English
• Subjects: Chromium; Damping; H infinity control; Neodymium; Partial differential equations
• DOI: 10.23919/ACC.1992.4792512

We study the linearised self-excited wave equation x tt - Δ x-P(x) x t =0, where P(x)≥0, P(x) L ∞ (Ω), in a bounded domain Ω ⊂ R n with smooth boundary Γ where boundary damping is present. Considering the partition {Γ + , Γ - } of the boundary Γ on which x=0 on Γ, and u n + Ku t + Lu= 0, on Γ, we find two different bounds for P such that the energy decays exponentially in the energy space as t tends to infinity (Here we assume Γ + ∩ Γ - = ø for n > 3). Both bounds depend on Ω (The domain of wave equation in R n , n ≥ 1). The second bound also depends on the feed-back functions K,L L ∞ (Γ + ) or more precisely depends on a positive function k(x) L ∞ (Γ + ) which determines K and L on the partition Γ + .