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arXiv · 1708.06300

Quantitative Approximation Properties for the Fractional Heat Equation

Angkana Rüland·Mikko Salo
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Abstract

In this note we analyse \emph{quantitative} approximation properties of a certain class of \emph{nonlocal} equations: Viewing the fractional heat equation as a model problem, which involves both \emph{local} and \emph{nonlocal} pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain \emph{qualitative} approximation results from \cite{DSV16}. Using propagation of smallness arguments, we then provide bounds on the \emph{cost} of approximate controllability and thus quantify the approximation properties of solutions to the fractional heat equation. Finally, we discuss generalizations of these results to a larger class of operators involving both local and nonlocal contributions.

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Angkana Rüland, Mikko Salo. 2017-08-21. Quantitative Approximation Properties for the Fractional Heat Equation. https://arxiv.org/abs/1708.06300

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