Hyperbolic equations in joined domains with boundary energy dissipation

This work deals with the asymptotic behavior of solutions of two hyperbolic equations coupled in series where the energy-absorbing boundaries are presented. It is shown that under some geometrical conditions with respect to a vector field h(x) in the joined surface of the two bounded domains in the space of Rⁿ, the energy of the system will decay uniformly exponentially. Some numerical results for different design of boundary controllers of rectangular domains are presented.