Formal asymptotics of bubbling in the harmonic map heat flow

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The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behavior of singularities arising in this flow for a special class of solutions which generalizes a known (radially symmetric) reduction. Specifically, the rate at which blowup occurs is investigated in settings with certain symmetries, using the method of matched asymptotic expansions. We identify a range of blowup scenarios in both finite and infinite time, including degenerate cases.
Original languageEnglish
Pages (from-to)1682-1717 (electronic)
JournalSIAM journal on applied mathematics
Issue number5
Publication statusPublished - 2003

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