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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
21 Aug 2017
|
| In: |
Arxiv
Year: 2017, Pages: 1-24 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1708.06300
|
| Author Notes: | Angkana Rüland and Mikko Salo |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1758990821 | ||
| 003 | DE-627 | ||
| 005 | 20220819214923.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 210526s2017 xx |||||o 00| ||eng c | ||
| 035 | |a (DE-627)1758990821 | ||
| 035 | |a (DE-599)KXP1758990821 | ||
| 035 | |a (OCoLC)1341414045 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Rüland, Angkana |d 1987- |e VerfasserIn |0 (DE-588)1051987679 |0 (DE-627)787342378 |0 (DE-576)407655506 |4 aut | |
| 245 | 1 | 0 | |a Quantitative approximation properties for the fractional heat equation |c Angkana Rüland and Mikko Salo |
| 264 | 1 | |c 21 Aug 2017 | |
| 300 | |a 24 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 26.05.2021 | ||
| 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. | ||
| 650 | 4 | |a Mathematics - Analysis of PDEs | |
| 700 | 1 | |a Salo, Mikko |d 1979- |e VerfasserIn |0 (DE-588)173729959 |0 (DE-627)698635841 |0 (DE-576)134570995 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Arxiv |d Ithaca, NY : Cornell University, 1991 |g (2017), Artikel-ID 1708.06300, Seite 1-24 |h Online-Ressource |w (DE-627)509006531 |w (DE-600)2225896-6 |w (DE-576)28130436X |7 nnas |a Quantitative approximation properties for the fractional heat equation |
| 773 | 1 | 8 | |g year:2017 |g elocationid:1708.06300 |g pages:1-24 |g extent:24 |a Quantitative approximation properties for the fractional heat equation |
| 856 | 4 | 0 | |u http://arxiv.org/abs/1708.06300 |x Verlag |z lizenzpflichtig |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20210526 | ||
| 993 | |a Article | ||
| 994 | |a 2017 | ||
| 998 | |g 1051987679 |a Rüland, Angkana |m 1051987679:Rüland, Angkana |p 1 |x j | ||
| 999 | |a KXP-PPN1758990821 |e 3931334953 | ||
| BIB | |a Y | ||
| JSO | |a {"person":[{"family":"Rüland","given":"Angkana","roleDisplay":"VerfasserIn","display":"Rüland, Angkana","role":"aut"},{"family":"Salo","given":"Mikko","display":"Salo, Mikko","roleDisplay":"VerfasserIn","role":"aut"}],"title":[{"title":"Quantitative approximation properties for the fractional heat equation","title_sort":"Quantitative approximation properties for the fractional heat equation"}],"recId":"1758990821","language":["eng"],"type":{"bibl":"chapter","media":"Online-Ressource"},"note":["Gesehen am 26.05.2021"],"name":{"displayForm":["Angkana Rüland and Mikko Salo"]},"id":{"eki":["1758990821"]},"origin":[{"dateIssuedKey":"2017","dateIssuedDisp":"21 Aug 2017"}],"relHost":[{"physDesc":[{"extent":"Online-Ressource"}],"origin":[{"dateIssuedDisp":"1991-","publisher":"Cornell University ; Arxiv.org","dateIssuedKey":"1991","publisherPlace":"Ithaca, NY ; [Erscheinungsort nicht ermittelbar]"}],"id":{"zdb":["2225896-6"],"eki":["509006531"]},"note":["Gesehen am 28.05.2024"],"disp":"Quantitative approximation properties for the fractional heat equationArxiv","type":{"bibl":"edited-book","media":"Online-Ressource"},"language":["eng"],"recId":"509006531","pubHistory":["1991 -"],"titleAlt":[{"title":"Arxiv.org"},{"title":"Arxiv.org e-print archive"},{"title":"Arxiv e-print archive"},{"title":"De.arxiv.org"}],"part":{"extent":"24","text":"(2017), Artikel-ID 1708.06300, Seite 1-24","pages":"1-24","year":"2017"},"title":[{"title_sort":"Arxiv","title":"Arxiv"}]}],"physDesc":[{"extent":"24 S."}]} | ||
| SRT | |a RUELANDANGQUANTITATI2120 | ||