dc.contributor.author Collot, Charles en dc.contributor.author Merle, Frank en dc.contributor.author Raphaël, Pierre en dc.date.accessioned 2020-01-18T00:30:28Z dc.date.available 2020-01-18T00:30:28Z dc.identifier.issn 0894-0347 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/301007 dc.description.abstract We 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.sponsorship ERC consolidator grant SingWaves dc.language en en dc.publisher American Mathematical Society (AMS) dc.rights All rights reserved dc.rights.uri dc.title Strongly anisotropic type II blow up at an isolated point en dc.type Article prism.endingPage 1 prism.publicationName Journal of the American Mathematical Society en prism.startingPage 1 dc.identifier.doi 10.17863/CAM.48083 dcterms.dateAccepted 2019-09-01 en rioxxterms.versionofrecord 10.1090/jams/941 en rioxxterms.version AM rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2019-09-01 en dc.identifier.eissn 1088-6834 rioxxterms.type Journal Article/Review en pubs.funder-project-id European Commission Horizon 2020 (H2020) ERC (SINGWAVES 646650) cam.issuedOnline 2019-10-25 en rioxxterms.freetoread.startdate 2020-10-25
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