On the $ω$-limit set of a nonlocal differential equation: application of rearrangement theory Article Swipe
We study the $ω$-limit set of solutions of a nonlocal ordinary differential equation, where the nonlocal term is such that the space integral of the solution is conserved in time. Using the monotone rearrangement theory, we show that the rearranged equation in one space dimension is the same as the original equation in higher space dimensions. In many cases, this property allows us to characterize the $ω$-limit set for the nonlocal differential equation. More precisely, we prove that the $ω$-limit set only contains one element.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1601.06491
- https://arxiv.org/pdf/1601.06491
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4293406746
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Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4293406746Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.1601.06491Digital Object Identifier
- Title
-
On the $ω$-limit set of a nonlocal differential equation: application of rearrangement theoryWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2016Year of publication
- Publication date
-
2016-01-25Full publication date if available
- Authors
-
Nam P. NguyenList of authors in order
- Landing page
-
https://arxiv.org/abs/1601.06491Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1601.06491Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1601.06491Direct OA link when available
- Concepts
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Limit (mathematics), Mathematics, Ordinary differential equation, Space (punctuation), Mathematical analysis, Differential equation, Omega, Monotone polygon, Limit set, Dimension (graph theory), Mathematical physics, Pure mathematics, Physics, Quantum mechanics, Geometry, Linguistics, PhilosophyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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