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 y(n) = Delta y + mu Delta y' with small damping constant mu > 0, in a bounded domain Omega in R-n under mixed undamped boundary conditions. A uniform exponential energy decay rate E(t) less than or equal to Me-beta tE(0) where M greater than or equal to 1 and beta = mu/mu(0), mu(0) being a quadratic function of mu, 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. (C) 1997 Academic Press.