On the Spectral Properties and Stabilization of Acoustic Flow

In this paper we use perturbation theory to study the spectral properties and energy decay of two dimensional acoustic ow (cf. Beale[1], Morse & Ingard[10]): tt c 2 = 0 in (0;1), m tt + d t + k = t and x = t on 0 (0;1), @ @ = 0 on 1 (0;1) with initial data (0) = 0; t(0) = 1 in and (0) = 0; t(0) = 1 on 0 where = (0; 1) (0; 1), 0 = f(1; y); 0 < y < 1g, 1 = @ n 0 and is the external normal direction on the boundary. Locations of eigenvalues of the in nitesimal generator of semigroup associated with the above system are estimated. A certain \Fourier" expansion are obtained. That the energy decays to zero and like t 1 (even like t ) if initial data satisfy certain smoothness are proved.