Quantitative approximation properties for the fractional heat equation
Rüland, Angkana; Salo, Mikko (2020). Quantitative approximation properties for the fractional heat equation. Mathematical Control and Related Fields, 10 (1), 1-26. DOI: 10.3934/mcrf.2019027
Published inMathematical Control and Related Fields
© 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
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Related funder(s)European Commission; Academy of Finland
Funding program(s)FP7 (EU's 7th Framework Programme); Centre of Excellence, AoF
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.