Archive for Rational Mechanics and Analysis

, Volume 161, Issue 2, pp 93–112

Nonuniqueness for the Heat Flow¶of Harmonic Maps on the Disk

  • Michiel Bertsch 
  • Roberta Dal Passo
  • Rein van der Hout

DOI: 10.1007/s002050100171

Cite this article as:
, M., Dal Passo, R. & van der Hout, R. Arch. Rational Mech. Anal. (2002) 161: 93. doi:10.1007/s002050100171

Abstract

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michiel Bertsch 
    • 1
  • Roberta Dal Passo
    • 1
  • Rein van der Hout
    • 2
  1. 1.Department of Mathematics¶University of Tor Vergata¶Via della Ricerca Scientifica¶00133 Roma, Italy¶e-mail: bertsch@mat.uniroma2.it¶e-mail: dalpasso@mat.uniroma2.itIT
  2. 2.Akzo Nobel Chemicals Research¶Arnhem, The Netherlands¶and Mathematical Institute¶University of Leiden¶Leiden, The Netherlands¶e-mail: rein.vanderhout@akzonobel.comNL