A vibrating plate is here taken to satisfy the model equation:*u*_{tt} + Δ^{2}u = 0 (where*Δ*^{2}u:= Δ(Δu); Δ = Laplacian) with boundary conditions of the form:*u*_{v} = 0 and*(Δu)*_{v} = ϕ = control. Thus, the state is the pair [*u, u*_{t}] and controllability means existence of*ϕ* on Σ:= (0,*T*)×*∂Ω* transfering ‘any’*[u, u*_{t}]_{0} to ‘any’*[u, u*_{t}]_{T}. The formulation is given by eigenfunction expansion and duality. The substantive results apply to a rectangular plate. For large*T* one has such controllability with*∥ϕ∥ = O(T*^{−1/2}). More surprising is that (based on a harmonic analysis estimate [11]) one has controllability for arbitrarily short times (in contrast to the wave equation:*u*_{tt} = Δu) with log*∥ϕ∥ = O(T*^{−1}) as*T*→0. Some related results on minimum time control are also included.

}, author = {Leugering, Günter and Krabs, W. and Seidman, Thomas I.}, doi = {10.1007/BF01442208}, faupublication = {no}, journal = {Applied Mathematics and Optimization}, pages = {205-229}, peerreviewed = {Yes}, title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {A} {VIBRATING} {PLATE}}, url = {http://link.springer.com/article/10.1007/BF01442208}, volume = {13}, year = {1985} }