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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2104.03689 |
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| _version_ | 1866910841237929984 |
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| author | Grafke, Tobias Scholtes, Sebastian Wagner, Alfred Westdickenberg, Maria G. |
| author_facet | Grafke, Tobias Scholtes, Sebastian Wagner, Alfred Westdickenberg, Maria G. |
| contents | We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in $d\geq 2$ and the critical parameter regime of large system size and mean value close to $-1$. We employ the String Method of E, Ren, and Vanden-Eijnden -- a numerical algorithm for computing transition pathways in complex systems -- in $d=2$ to gain additional insight into the properties of the minima and saddle point. Motivated by the numerical observations, we adapt a method of Caffarelli and Spruck to study convexity of level sets in $d\geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_03689 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Numerics and analysis of Cahn--Hilliard critical points Grafke, Tobias Scholtes, Sebastian Wagner, Alfred Westdickenberg, Maria G. Analysis of PDEs Numerical Analysis 35B38, 49J40 We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in $d\geq 2$ and the critical parameter regime of large system size and mean value close to $-1$. We employ the String Method of E, Ren, and Vanden-Eijnden -- a numerical algorithm for computing transition pathways in complex systems -- in $d=2$ to gain additional insight into the properties of the minima and saddle point. Motivated by the numerical observations, we adapt a method of Caffarelli and Spruck to study convexity of level sets in $d\geq 2$. |
| title | Numerics and analysis of Cahn--Hilliard critical points |
| topic | Analysis of PDEs Numerical Analysis 35B38, 49J40 |
| url | https://arxiv.org/abs/2104.03689 |