Exponential Energy Decay Estimate for the Solutions of Internally Damped Wave Equation in a Bounded Domain

AbstractHere we are concerned about the stability of the solution of internally damped wave equationy″=Δy+μΔy′ with small damping constant μ>0, in a bounded domain Ω inRnunder mixed undamped boundary conditions. A uniform exponential energy decay rateE(t)≤Me−βtE(0) whereM≥1 and β=μ/μ0, μ0being a quadratic function of μ, is proved for the solution of this type of boundary value problem. Earlier authors have considered the undamped wave equation with certain forms of damped boundary conditions proving similar and faster energy decay rates