Quantitative approximation properties for the fractional heat equation
Rüland, A., & Salo, M. (2020). Quantitative approximation properties for the fractional heat equation. Mathematical Control and Related Fields, 10(1), 1-26. https://doi.org/10.3934/mcrf.2019027
Published inMathematical Control and Related Fields
DisciplineInversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematics
© 2019 American Institute of Mathematical Sciences
In this article we analyse quantitative approximation properties of a certain class of nonlocal equations: Viewing the fractional heat equation as a model problem, which involves both local and 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 qualitative approximation results from . Using propagation of smallness arguments, we then provide bounds on the 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.
PublisherAmerican Institute of Mathematical Sciences
Publication in research information system
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Related funder(s)Academy of Finland; European Commission
Funding program(s)Centre of Excellence, AoF; FP7 (EU's 7th Framework Programme)
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingSuomen Akatemia 284715; European Commission 307023
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