New blow-up rates for fast controls of Schrödinger and heat equations

Gerald Tenenbaum 1 Marius Tucsnak 1, 2
2 CORIDA - Robust control of infinite dimensional systems and applications
IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est
Abstract : We consider the null-controllability problem for the Schrödinger and heat equations with boundary control. We concentrate on short-time, or fast, controls. We improve recent estimates of Miller on the norm of the operator associating to any initial state the minimal norm control driving the system to zero. Our main results concern the Schrödinger and heat equations in one space dimension. They yield new estimates concerning window problems for series of exponentials as described by Seidman, Avdonin and Ivanov \cite{Seid1}. These results are used to deal with the case of several space dimensions.
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Gerald Tenenbaum, Marius Tucsnak. New blow-up rates for fast controls of Schrödinger and heat equations. Journal of Differential Equations, Elsevier, 2007, 243 (1), pp.70--100. ⟨10.1016/j.jde.2007.06.019⟩. ⟨hal-00140540v2⟩



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