Energy decay for the linear Klein–Gordon equation and boundary control

In this work we study the asymptotic behavior of the solutions of the linear Klein–Gordon equation in R N , N ⩾ 1 . We prove that local energy of solutions to the Cauchy problem decays polynomially. Afterwards, we use the local decay of energy to study exact boundary controllability for the linear Klein–Gordon equation in general bounded domains of R N , N ⩾ 1 .