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Please use this identifier to cite or link to this item: https://digital.lib.ueh.edu.vn/handle/UEH/73643
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dc.contributor.authorGiao Ky Duong-
dc.contributor.otherTej-Eddine Ghoul-
dc.contributor.otherHatem Zaag-
dc.date.accessioned2025-01-21T04:12:22Z-
dc.date.available2025-01-21T04:12:22Z-
dc.date.issued2023-
dc.identifier.issn1078-0947 (Print), 1553-5231 (Online)-
dc.identifier.urihttps://digital.lib.ueh.edu.vn/handle/UEH/73643-
dc.description.abstractIn this paper, we consider the standard semilinear heat equation ∂tu=Δu+|u|p−1u,p>1.The determination of the (believed to be) generic blowup profile is well established in the literature, with the solution blowing up only at one point. Though the blow-up of the gradient of the solution is a direct consequence of the single-point blow-up property and the mean value theorem, there is no determination of the final blowup profile for the gradient in the literature, up to our knowledge. In this paper, we refine the construction technique of Bricmont-Kupiainen and Merle-Zaag , and derive the following profile for the gradient: ∇u(x,T)∼−2bp−1x|xen
dc.description.abstractln⁡|xen
dc.description.abstract[b|x|22|ln⁡|xen
dc.description.abstract]−p+12(p−1) as x→0, where b=(p−1)24p, which is as expected the gradient of the well-known blowup profile of the solution.en
dc.language.isoeng-
dc.publisherAmerican Institute of Mathematical Sciences-
dc.relation.ispartofDCDS-
dc.relation.ispartofseriesVol. 44, Issue 4-
dc.rights2025 American Institute of Mathematical Sciences-
dc.subjectSemilinear heat equationen
dc.titleGradient blowup profile for the semilinear heat equationen
dc.typeJournal Articleen
dc.identifier.doihttps://doi.org/10.3934/dcds.2023136-
dc.format.firstpage997-
dc.format.lastpage1025-
ueh.JournalRankingISI, Scopus-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextnone-
item.languageiso639-1en-
item.fulltextOnly abstracts-
item.openairetypeJournal Article-
item.cerifentitytypePublications-
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