ON THE ENERGY DECAY OF 2 COUPLED STRINGS THROUGH A JOINT DAMPER

The stabilization of two coupled strings with fixed boundaries attache d to a linear damper at their joint of connection is studied. The tran sformation used in a previous approach to convert the second order hyp erbolic equations into a first order system results in a loss of equiv alence. It is shown that when the ratio of the wave speeds of the two strings is an irrational number, the system is asymptotically but not exponentially, stable. The method is applied to the other cases with d ifferent joint and boundary conditions. (C) 1997 Academic Press Limite d.