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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 },
pages = {781--796},
publisher = {EDP-Sciences},
volume = {39},
number = {4},
year = {2005},
doi = {10.1051/m2an:2005034},
mrnumber = {2165679},
zbl = {1078.35008},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005034/}
}
TY - JOUR AU - Merlet, Benoit AU - Pierre, Morgan TI - Moving mesh for the axisymmetric harmonic map flow JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2005 SP - 781 EP - 796 VL - 39 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005034/ DO - 10.1051/m2an:2005034 LA - en ID - M2AN_2005__39_4_781_0 ER -
%0 Journal Article %A Merlet, Benoit %A Pierre, Morgan %T Moving mesh for the axisymmetric harmonic map flow %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2005 %P 781-796 %V 39 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005034/ %R 10.1051/m2an:2005034 %G en %F M2AN_2005__39_4_781_0
Merlet, Benoit; Pierre, Morgan. Moving mesh for the axisymmetric harmonic map flow. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 4, pp. 781-796. doi: 10.1051/m2an:2005034
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