Beschreibung:
<jats:p>Abstract The finite time stabilizability of the one dimensional heat equation is proved by Coron–Nguyên [16], while the same question for multidimensional spaces remained open. Inspired by Coron–Trélat [17] we introduce a new method to stabilize multidimensional heat equations quantitatively in finite time and call it Frequency Lyapunov method. This method naturally combines spectral inequality [35] and constructive feedback stabilization. As application this approach also yields a constructive proof for null controllability, which gives sharing optimal cost with explicit controls and works perfectly for related nonlinear models such as Navier–Stokes equations [52].</jats:p>