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arXiv · 2401.17349

Sharp estimates of the one-dimensional boundary control cost for parabolic systems

Manuel González-Burgos·Lydia Ouaili
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Abstract

In this work we present new results on the cost of the boundary controllability of parabolic systems at time $T > 0$. In particular, we will study optimal estimates of the control cost at time $T$ ($T$ small enough) when the eigenvalues of the generator of the $C_0$ semigroup accumulate and do not satisfy a gap condition. The main ingredient we will use is the moment method combined with sharp estimates of the $L^2(0,T; \mathbb C)$-norm of the elements of biorthogonal families to complex exponentials.

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Manuel González-Burgos, Lydia Ouaili. 2024-01-30. Sharp estimates of the one-dimensional boundary control cost for parabolic systems. https://doi.org/10.1090/conm%2F757%2F15247

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