Stabilization of coupled hyperbolic equations in series for a higher dimensional space by energy absorbing boundaries

Abstract

Energy decay estimaks for a system of two hyperbolic equations coupled in series with boundary dissipation are studied. It is shown that under certain conditions in the joined surface of the two bounded domains of the equations in the space of R", the energy of the system will decay uniformly exponentially. J ( t ) =/u1[2m-Vu+(nl)u]dz+ 9[2m. Vu+("-1)uJdz. (2.3)Our goal is to prove existence of €0, a1,a2 such that (2.4) @ -E ( <al&E, f o r t ? 0, &>O, andrzS&@ 9 5 -a& for f 0. (2.5) Then, from (2.4) and (2.5) we obtain the desired result. In order to verify (2.4). first consider the Poincare's inequality with respect to each 01 91 -221 6/93/$3.00 (8 1993 IEEE