| R^3中几类半线性非局部方程解的一维对称性结果 | |
| Alternative Title | A One-Dimensional Symmetry Result for a few class of Semilinear Nonlocal Equations in R^3 |
| 刘家熙 | |
| Thesis Advisor | 李万同 |
| 2019-04-02 | |
| Degree Grantor | 兰州大学 |
| Place of Conferral | 兰州 |
| Degree Name | 硕士 |
| Degree Discipline | 应用数学 |
| Keyword | 非局部算子 Allen-Cahn方程 非局部能量 De Giorgi猜想 一维对称性 Liouville型结果 |
| Abstract | 本文的目标是得到三维欧式空间中带有不同核函数的几类非局部Allen-Cahn方程的解的一维对称性结果。首先考虑三维欧式空间中带有紧支集核函数的非局部算子对应的非局部Allen-Cahn方程 单调有界Layer-解的一维对称性，然后将结果推广到有限个带有紧支集的核的非局部算子相加得到的和算子对应的非局部半线性方程，最后讨论三维欧式空间中分数阶Allen-Cahn方程的单调有界解的一维对称性。类似于经典Allen-Cahn方程在三维欧式空间中的解的一维对称性的证明方法，本文的证明过程中主要利用了对非局部能量泛函的估计以及近期由Hamel等人得到的非局部算子的Liouville型结果。 |
| Other Abstract | The aim of this paper is to obtain a one-dimensional symmetry result for a few class of nonlocal Allen-Cahn equations with different kernels in R^3.Firstly, we consider the nonlocal Allen-Cahn equation corresponding to nonlocal operators with compact support kernels in R^3. The results then are extended to the sum of a finite number of nonlocal operators with compact support. Finally, the one-dimensional symmetry result for monotone bounded solutions of fractional Allen-Cahn equation in R^3 is discussed. Similar to the proof of the one-dimensional symmetry result for the classical Allen-Cahn equation in R^3, in our proof we mainly use the estimates for nonlocal energy and a Liouville type result for nonlocal operators obtained by Hamel et al recently. |
| Pages | 46 |
| URL | 查看原文 |
| Language | 中文 |
| Document Type | 学位论文 |
| Identifier | https://ir.lzu.edu.cn/handle/262010/342260 |
| Collection | 数学与统计学院 |
| Affiliation | 数学与统计学院 |
| First Author Affilication | School of Mathematics and Statistics |
| Recommended Citation GB/T 7714 | 刘家熙. R^3中几类半线性非局部方程解的一维对称性结果[D]. 兰州. 兰州大学,2019. |
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