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A deterministic optimal design problem for the heat equation. (English) Zbl 1353.35315

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

MSC:

35R30 Inverse problems for PDEs
58J35 Heat and other parabolic equation methods for PDEs on manifolds
93B07 Observability
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