On the optimality of the observability inequalities for Kirchhoff plate systems with potentials in unbounded domains∗

In this paper, we derive a sharp observability inequality for Kirchhoff plate equations with lower order terms in an unbounded domain Ω of lR. More precisely, when the observation is assumed to be located in a subdomain ω such that Ω \ ω is bounded and the observation time T > 0 is sufficiently large, we establish an observability estimate with an explicit observability constant for Kirchhoff plate systems with an arbitrary finite number of components and in any space dimension with lower order bounded potentials. Also, when Ω = lR, by means of the Meshkov construction for the bi-Laplacian equation, we prove the optimality of this estimate for systems of more than two components and in even space dimensions n ≥ 2.