On the Spectral Properties and Stabilization of Acoustic Flow
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 flow (cf. [J.T. Beale, Indiana Univ. Math. J., 25 (1976), pp.895--917], [P.M. Morse and K.U. Ingard, Theoretical Acoustics, McGraw-Hill, New York, 1968]):$\phi_{tt}-c^2\Delta \phi=0$ in $\Omega\times(0,\infty)$, $m\delta_{tt}+d\delta_t+k\delta=-\rho\phi_t$ and $\phi_x=\delta_t$ on $\Gamma_0\times(0,\infty)$, $\frac{\partial\phi}{\partial\nu}=0$ on …