Quantitative approximation properties for the fractional heat equation
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 proper...
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| Main Authors: | , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
21 Aug 2017
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| In: |
Arxiv
Year: 2017, Pages: 1-24 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1708.06300
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| Author Notes: | Angkana Rüland and Mikko Salo |
MARC
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| 520 | |a 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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