Quantitative approximation properties for the fractional heat equation
<p style='text-indent:20px;'>In this article we analyse <i>quantitative</i> approximation properties of a certain class of <i>nonlocal</i> equations: Viewing the fractional heat equation as a model problem, which involves both <i>local</i> and <...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
March 2020
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| In: |
Mathematical control and related fields
Year: 2020, Volume: 10, Issue: 1, Pages: 1-26 |
| ISSN: | 2156-8499 |
| DOI: | 10.3934/mcrf.2019027 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.3934/mcrf.2019027 Verlag, lizenzpflichtig, Volltext: https://www.aimsciences.org/article/doi/10.3934/mcrf.2019027 
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| Author Notes: | Angkana Rüland, Mikko Salo |
| Summary: | <p style='text-indent:20px;'>In this article we analyse <i>quantitative</i> approximation properties of a certain class of <i>nonlocal</i> equations: Viewing the fractional heat equation as a model problem, which involves both <i>local</i> and <i>nonlocal</i> pseudodifferential operators, we study quantitative approximation properties of solutions to it. First, relying on Runge type arguments, we give an alternative proof of certain <i>qualitative</i> approximation results from [<xref ref-type="bibr" rid="b9">9</xref>]. Using propagation of smallness arguments, we then provide bounds on the <i>cost</i> 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.</p> |
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| Item Description: | Gesehen am 26.05.2021 |
| Physical Description: | Online Resource |
| ISSN: | 2156-8499 |
| DOI: | 10.3934/mcrf.2019027 |