Author

P. Lissy

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Preprint Aug 2026

Optimal cost of fast boundary controls for the one-dimensional heat equation

We consider the heat equation on $(0,L)$ with homogeneous Dirichlet condition at one endpoint and a Dirichlet boundary control at the other. If $C_{\mathrm H}(T,L)$ denotes the optimal $L^2$ null-control cost for initial data in $H^{-1}(0,L)$, we prove that \[ C_{\mathrm H}(T,L) = \exp\left(\frac{\kappa_*L^2+o(1)...

P. Lissy · 2 citations · ⚡1