Title: Boundary value controllability and observability problems for the wave and heat equation
Abstract: Abstract In this paper, we study controllability and observability problems for the wave and heat equation in a spherical region in R n , where the control enters in the mixed boundary condition. In the main result, we show that all “finite energy” initial states (i.e. (ω 0 , ν 0 ) ∈ H 1 (Ω) × L 2 (Ω)) can be steered to zero at time T , using a control f ∈ L 2 (∂Ω × [0, T ]), provided T > 2. On this basis, we use the duality principle to investigate initial observability for the wave equation. Applying the Fourier transform technique, we obtain controllability and observability results for the heat equation.