Nonuniqueness for the Heat Flow¶of Harmonic Maps on the Disk
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- , M., Dal Passo, R. & van der Hout, R. Arch. Rational Mech. Anal. (2002) 161: 93. doi:10.1007/s002050100171
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We prove that for suitable initial data the heat flow of harmonic maps, from the disk to the sphere, admits infinitely many solutions, characterised by “backward bubbling” at some arbitrarily large time, all having uniformly bounded energy.