On the blow-up of heat flow for conformal 3-harmonic maps
On the blow-up of heat flow for conformal 3-harmonic maps
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关于共形 3 次谐波映射的热流爆炸
DOI：
10.1090/s0002-9947-02-03054-4
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发表时间：
2002
影响因子：
1.3
通讯作者：
C. Law
中科院分区：
文献类型：
--
作者：
Chao;L. Cheung;Y. Choi;C. Law
Chang，Ding，and Ye（1992）利用比较定理证明了在一定的初边值条件下，从D2（R2中的单位球）到S2（R3中的单位球）的调和映射的热流的有限时间导数blow-up.我们把这个结果推广到了从D3到S3的3-调和映射热流的情形.与前一种情况相比，我们的控制抛物方程是拟线性的和退化的。诸如发展新的比较定理等技术问题必须解决。
Using a comparison theorem, Chang, Ding, and Ye (1992) proved a finite time derivative blow-up for the heat flow of harmonic maps from D 2 (a unit ball in R 2 ) to S 2 (a unit sphere in R 3 ) under certain initial and boundary conditions. We generalize this result to the case of 3-harmonic map heat flow from D 3 to S 3 . In contrast to the previous case, our governing parabolic equation is quasilinear and degenerate. Technical issues such as the development of a new comparison theorem have to be resolved.