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Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions
Journal
Nonlinearity
35
Author
Biernat Paweł
Volume
28
Issue
1
Pages
167-185
ISSN
0951-7715
eISSN
1361-6544
Keywords in English
type II
matched asymptotics
singularity
parabolic
harmonic map flow
Language
English
Container language
English
Abstract in English
We analyse the finite-time blow-up of solutions of the heat flow for k-corotational maps
Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
cris.lastimport.scopus | 2024-04-07T18:00:45Z | |
dc.abstract.en | We analyse the finite-time blow-up of solutions of the heat flow for k-corotational maps $\mathbb{R}^{d}\rightarrow S^{d}$. For each dimension $d> 2+k\left ( 2+2\sqrt{2} \right )$ we construct a countable family of blow-up solutions via a method of matched asymptotics by glueing a re-scaled harmonic map to the singular self-similar solution: the equatorial map. We find that the blow-up rates of the constructed solutions are closely related to the eigenvalues of the self-similar solution. In the case of 1-corotational maps our solutions are stable and represent the generic blow-up. | pl |
dc.affiliation | Wydział Matematyki i Informatyki : Instytut Matematyki | pl |
dc.contributor.author | Biernat, Paweł - 106913 | pl |
dc.date.accessioned | 2015-07-16T13:40:36Z | |
dc.date.available | 2015-07-16T13:40:36Z | |
dc.date.issued | 2015 | pl |
dc.description.admin | [AA] Biernat, Paweł | |
dc.description.number | 1 | pl |
dc.description.physical | 167-185 | pl |
dc.description.publication | 1 | pl |
dc.description.volume | 28 | pl |
dc.identifier.doi | 10.1088/0951-7715/28/1/167 | pl |
dc.identifier.eissn | 1361-6544 | pl |
dc.identifier.issn | 0951-7715 | pl |
dc.identifier.uri | http://ruj.uj.edu.pl/xmlui/handle/item/13084 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights | Dodaję tylko opis bibliograficzny | * |
dc.rights.licence | bez licencji | |
dc.rights.uri | * | |
dc.subject.en | type II | pl |
dc.subject.en | matched asymptotics | pl |
dc.subject.en | singularity | pl |
dc.subject.en | parabolic | pl |
dc.subject.en | harmonic map flow | pl |
dc.subtype | Article | pl |
dc.title | Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions | pl |
dc.title.journal | Nonlinearity | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |
Affiliations
Wydział Matematyki i Informatyki
Biernat, Paweł