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Leveraging on the work of De Vore and Zuazua, we further explore theirmethodology and deal with two open questions presented in their paper. We showthat for a class of linear evolutionary PDEs the admissible choice of relevantparameters used to construct the near-optimal sampling sequence is notinfluenced by the spectrum of of the operator controlling the spatial part ofthe PDE, but only by its order. Furthermore, we show that it is possible toextend their algorithm to a simple version of a non-autonomous heat equation inwhich the heat diffusivity coefficient depends explicitly on time.

On near-optimal time samplings for initial data best approximation