Formal Asymptotics of Bubbling in the Harmonic Map Heat Flow

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 rat...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 63; no. 5; pp. 1682 - 1717
Main Authors Jan Bouwe van den Berg, Hulshof, Josephus, King, John R.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2003
Subjects
A priori knowledge
Algebra
Applied mathematics
Approximation
Boundary conditions
Coordinate systems
Crystals
Energy
Heat transfer
Infinity
Liquid crystals
Polynomials
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Summary: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.
ISSN:0036-1399
1095-712X
DOI:10.1137/s0036139902408874