We build corotational symmetric solutions to the harmonic map flow from the unit disc into the unit sphere which have constant degree. First, we prove the existence of such solutions, using a time semi-discrete scheme based on the idea that the harmonic map flow is the -gradient of the relaxed Dirichlet energy. We prove a partial uniqueness result concerning these solutions. Then, we compute numerically these solutions by a moving-mesh method which allows us to deal with the singularity at the origin. We show numerical evidence of the convergence of the method.
@article{M2AN_2005__39_4_781_0,
author = {Merlet, Benoit and Pierre, Morgan},
title = {Moving mesh for the axisymmetric harmonic map flow},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {39},
year = {2005},
pages = {781-796},
doi = {10.1051/m2an:2005034},
mrnumber = {2165679},
zbl = {1078.35008},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2005__39_4_781_0}
}
Merlet, Benoit; Pierre, Morgan. Moving mesh for the axisymmetric harmonic map flow. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 781-796. doi : 10.1051/m2an:2005034. http://gdmltest.u-ga.fr/item/M2AN_2005__39_4_781_0/
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