engleski

Null-controllability of the heat equation in unbounded domains

We adapt a strategy for proving null-controllability of parabolic equations by [Tenenbaum-Tucsnak-2011] to a setting of lower semibounded operator swith continuous spectrum. This includes in particular the case of the controlled heat equation in Rd where the diffusion term −∆ is replaced by a Schrödinger operator −∆+V. We lay particular emphasis on explicitly estimating the control cost in terms of all occurring model parameters. This is then combined with recent scale-free unique continuation principles for spectral subspaces of Schrödinger operators and the behaviour of the control cost in certain (homogenization)limits is studied. The talk is based on the joint work with Matthias Täufer, Martin Tautenhahn and Ivan Veselić.

null-controllability, parabolic equations, control cost

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