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Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions

2015
journal article
article
10.1088/0951-7715/28/1/167
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 . For each dimension 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.

Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.abstract.enWe 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.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorBiernat, Paweł - 106913 pl
dc.date.accessioned2015-07-16T13:40:36Z
dc.date.available2015-07-16T13:40:36Z
dc.date.issued2015pl
dc.description.admin[AA] Biernat, Paweł
dc.description.number1pl
dc.description.physical167-185pl
dc.description.publication1pl
dc.description.volume28pl
dc.identifier.doi10.1088/0951-7715/28/1/167pl
dc.identifier.eissn1361-6544pl
dc.identifier.issn0951-7715pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/13084
dc.languageengpl
dc.language.containerengpl
dc.rightsDodaję tylko opis bibliograficzny*
dc.rights.licencebez licencji
dc.rights.uri*
dc.subject.entype IIpl
dc.subject.enmatched asymptoticspl
dc.subject.ensingularitypl
dc.subject.enparabolicpl
dc.subject.enharmonic map flowpl
dc.subtypeArticlepl
dc.titleNon-self-similar blow-up in the heat flow for harmonic maps in higher dimensionspl
dc.title.journalNonlinearitypl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
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.
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Biernat, Paweł - 106913
dc.date.accessioned
2015-07-16T13:40:36Z
dc.date.available
2015-07-16T13:40:36Z
dc.date.issuedpl
2015
dc.description.admin
[AA] Biernat, Paweł
dc.description.numberpl
1
dc.description.physicalpl
167-185
dc.description.publicationpl
1
dc.description.volumepl
28
dc.identifier.doipl
10.1088/0951-7715/28/1/167
dc.identifier.eissnpl
1361-6544
dc.identifier.issnpl
0951-7715
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/13084
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Dodaję tylko opis bibliograficzny
dc.rights.licence
bez licencji
dc.rights.uri*
dc.subject.enpl
type II
dc.subject.enpl
matched asymptotics
dc.subject.enpl
singularity
dc.subject.enpl
parabolic
dc.subject.enpl
harmonic map flow
dc.subtypepl
Article
dc.titlepl
Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions
dc.title.journalpl
Nonlinearity
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations
Wydział Matematyki i Informatyki
Biernat, Paweł

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