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dc.contributor.authorCollot, Charlesen
dc.contributor.authorMerle, Franken
dc.contributor.authorRaphaël, Pierreen
dc.date.accessioned2020-01-18T00:30:28Z
dc.date.available2020-01-18T00:30:28Z
dc.identifier.issn0894-0347
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/301007
dc.description.abstractWe consider the energy super critical $d+1$ dimensional semilinear heat equation $$\pa_tu=\Delta u+u^{p}, \ \ x\in \Bbb R^{d+1}, \ \ p\geq 3, \ d\geq 14.$$ A fundamental open problem on this canonical nonlinear model is to understand the possible blow up profiles appearing after renormalization of a singularity. We exhibit in this paper a new scenario corresponding to the first example of strongly anisotropic blow up bubble: the solution displays a completely different behaviour depending on the considered direction in space. A fundamental step of the analysis is to solve the {\it reconnection problem} in order to produce finite energy solutions which is the heart of the matter. The corresponding anistropic mechanism is expected to be of fundamental importance in other settings in particular in fluid mechanics. The proof relies on a new functional framework for the construction and stabilization of type II bubbles in the parabolic setting using energy estimates only, and allows us to exhibit new unexpected blow up speeds.
dc.description.sponsorshipERC consolidator grant SingWaves
dc.languageenen
dc.publisherAmerican Mathematical Society (AMS)
dc.rightsAll rights reserved
dc.rights.uri
dc.titleStrongly anisotropic type II blow up at an isolated pointen
dc.typeArticle
prism.endingPage1
prism.publicationNameJournal of the American Mathematical Societyen
prism.startingPage1
dc.identifier.doi10.17863/CAM.48083
dcterms.dateAccepted2019-09-01en
rioxxterms.versionofrecord10.1090/jams/941en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-09-01en
dc.identifier.eissn1088-6834
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) ERC (SINGWAVES 646650)
cam.issuedOnline2019-10-25en
rioxxterms.freetoread.startdate2020-10-25


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