The paper deals with the well–posedness of the problem 8 >< >: utt −∆u = 0 in R× Ω, utt = kuν on R× Γ, u(0, x) = u0(x), ut(0, x) = v0(x) in Ω, where u = u(t, x), t ∈ R, x ∈ Ω, ∆ = ∆x denotes the Laplacian operator respect to the space variable, Ω is a bounded regular (C∞) open domain of RN (N ≥ 1), Γ = ∂Ω, ν is the outward normal to Ω, k is a constant. We prove that it is ill–posed if N ≥ 2, wh...