Nonuniqueness for the heat flow of harmonic maps on the disk

被引：46

作者：

Bertsch, M

Dal Passo, R

Van der Hout, R

机构：

[1] Univ Roma Tor Vergata, Dept Math, I-00133 Rome, Italy

[2] Leiden Univ, Math Inst, Leiden, Netherlands

[3] Akzo Nobel Chem Res, Arnhem, Netherlands

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2002年 / 161卷 / 02期

关键词：

D O I：

10.1007/s002050100171

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：93 / 112

页数：20

共 50 条

[21] Heat flow of harmonic maps from noncompact manifolds
WANG Meng1 LIU Xiao-feng21 Dept.of Math.
Applied Mathematics:A Journal of Chinese Universities(Series B), 2008, (04) : 431 - 436
[22] Removability of the singular set of the heat flow of harmonic maps
Chen, YM
Flaminio, L
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (02) : 513 - 525
[23] Heat flow of harmonic maps from noncompact manifolds
Meng Wang
Xiao-feng Liu
Applied Mathematics-A Journal of Chinese Universities, 2008, 23 : 431 - 436
[24] The heat flow of harmonic maps from noncompact manifolds
Jiayu L.
Silei W.
Chinese Annals of Mathematics, 2000, 21 (1) : 121 - 130
[25] Reverse bubbling and nonuniqueness in the harmonic map flow
Topping, P
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2002, 2002 (10) : 505 - 520
[26] Some new examples for nonuniqueness of the evolution problem of harmonic maps
Hong, MC
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 1998, 6 (04) : 809 - 818
[27] Partial regularity of the heat flow of half-harmonic maps and applications to harmonic maps with free boundary
Hyder, Ali
Segatti, Antonio
Sire, Yannick
Wang, Changyou
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2022, 47 (09) : 1845 - 1882
[28] NONUNIQUENESS OF THE HEAT FLOW OF DIRECTOR FIELDS
Primi, I.
ADVANCES IN DIFFERENTIAL EQUATIONS, 2010, 15 (3-4) : 349 - 380
[29] Regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps
Moser, R
MATHEMATISCHE ZEITSCHRIFT, 2003, 243 (02) : 263 - 289
[30] Regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps
Roger Moser
Mathematische Zeitschrift, 2003, 243 : 263 - 289

← 1 2 3 4 5 →