LAUSR

We study time decay of the energy for the one dimensional damped Klein-Gordon equation. We give an explicit necessary and sufficient condition on the continuous damping function $$\gamma \ge 0$$γ≥0 for which the energy $$\begin{aligned} E(t)=\int _{-\infty }^\infty |u_x|^2+|u|^2+ |u_t|^2 dx \end{aligned}$$E(t)=∫-∞∞|ux|2+|u|2+|ut|2dxdecays, whenever $$(u(0), u_t(0))\in H^2(\mathbb R)\times H^1(\mathbb R)$$(u(0),ut(0))∈H2(R)×H1(R).