A1 Journal article (refereed)
Quantitative approximation properties for the fractional heat equation (2020)


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


JYU authors or editors


Publication details

All authors or editors: Rüland, Angkana; Salo, Mikko

Journal or series: Mathematical Control and Related Fields

ISSN: 2156-8472

eISSN: 2156-8499

Publication year: 2020

Volume: 10

Issue number: 1

Pages range: 1-26

Publisher: American Institute of Mathematical Sciences

Publication country: United States

Publication language: English

DOI: http://doi.org/10.3934/mcrf.2019027

Open Access: Publication channel is not openly available

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/66751

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1708.06300


Abstract

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 [9]. 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.


Keywords: inverse problems; partial differential equations; approximation

Free keywords: fractional parabolic Calderón problem; Runge approximation: weak unique continuation; cost of approximation: nonlocal operators


Contributing organizations


Related projects

Centre of Excellence in Inverse Problems Research
Salo, Mikko
Academy of Finland
01/01/2015-31/12/2017


Ministry reporting: Yes

Reporting Year: 2020

Preliminary JUFO rating: 1


Last updated on 2020-18-08 at 13:00