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

Here we are concerned about the stability of the solution of internally damped wave equation yYsD yqm D yX with small damping constant m )0, in a bounded domain V in Rn under mixed undamped boundary conditions. A uniform expo- nential energy decay rate E t.FMeyb tE 0. where MG1 and b smrm0, m0 being a quadratic function of m, 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