Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778346 | Advances in Mathematics | 2017 | 67 Pages |
Abstract
In this paper, we study axially symmetric solutions of Allen-Cahn equation in the three dimensional Euclidean space. Using a sophisticated continuation method, we show the existence of a complete family of axially symmetric solutions with a range of logarithmic growth rates, which may be regarded as the analogue of the family of catenoids and hence called two-end solutions. Nonexistence of two-end solution with a small growth rate is also shown, which differs from the theory of minimal surfaces.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Changfeng Gui, Yong Liu, Juncheng Wei,