Traveling wave solutions of harmonic heat flow

被引：6
|
作者：
Bertsch, M.
Muratov, C. B.
Primi, I.
机构：
[1] CNR, Ist Appl Calcolo Mauro Picone, I-00161 Rome, Italy
[2] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy
[3] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA
[4] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, I-00185 Rome, Italy
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2006年 / 26卷 / 04期
关键词：
harmonic map; director field; traveling wave; singularity; calculus of variations; bistable potential;
D O I：
10.1007/s00526-006-0016-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove the existence of a traveling wave solution of the equation u(t) = Delta u + vertical bar del u vertical bar(2)u in an infinitely long cylinder of radius R, which connects two locally stable and axially symmetric steady states at x(3) = +/-infinity. Here a is a director field with values in S-2 subset of R-3: vertical bar u vertical bar = 1. The traveling wave has a singular point on the cylinder axis. Letting R -> infinity we obtain a traveling wave defined in all space.
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页码：489 / 509
页数：21
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