On near-optimal time samplings for initial data best approximation
Abstract
Leveraging on the work of DeVore and Zuazua, we further explore their methodology and deal with two openquestions presented in their paper. We show that for a class of linear evolutionary PDEs of order $2N$
the admissible choice of the parameter $\rho$ which is used to construct the near-optimal sampling sequence
is not influenced by the spectrum of of the operator controlling the spatial part of the PDE, but only by its order.
Furthermore, we show that it is possible to extend their algorithm to a simple version of a non-autonomous heat
equation in which the heat diffusivity coefficient depends explicitly on time.
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