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arXiv · 1506.06937

A deterministic optimal design problem for the heat equation

Heiko Gimperlein·Alden Waters
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Abstract

For the heat equation on a bounded subdomain $Ω$ of $\mathbb{R}^d$, we investigate the optimal shape and location of the observation domain in observability inequalites. A new decomposition of $L^2(\mathbb{R}^d)$ into heat packets allows us to remove the randomisation procedure and assumptions on the geometry of $Ω$ in previous works. The explicit nature of the heat packets gives new information about the observability constant in the inverse problem.

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Heiko Gimperlein, Alden Waters. 2016-05-17. A deterministic optimal design problem for the heat equation. https://arxiv.org/abs/1506.06937

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