双稳型Allen-Cahn方程的棱锥波和广义棱锥波 Alternative Title Traveling fronts of pyramidal shapes and general pyramidal shapes in the bisable Allen-Cahn equation 韩帮胜 Thesis Advisor 李万同 2013-05-24 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword Allen-Cahn方程 棱锥波 广义棱锥波 指数渐近稳定性 存在性 Abstract 本文主要研究了Allen-Cahn方程 ∂u/∂t= △u + f(u), (x, y, z) ∈ R3, t > 0,u|t=0= φ(x, y, z), (x, y, z) ∈ R3 在双稳情形下的棱锥波的渐近稳定性和广义棱锥波的存在性.主要内容分两章阐述. 首先对三维棱锥波的稳定性作进一步的研究,利用比较原理结合挤压技术得到 了Allen-Cahn 方程的三维棱锥波的全局指数渐近稳定性,并给出了明确的渐近传播 速度. 其次,我们将现有的三维棱锥波作进一步推广,得到了一般情形下的三维空间中 的广义棱锥波,并证明了在一般情形下这种广义棱锥波的存在性.这对研究行波解的 分类,尤其是高维行波解的分类迈出了新的一步. Other Abstract In this paper,we study the asymptotic stability of pyramid wave and the existence of general pyramid wave in the Allen-Cahn equation  ∂u/∂t= △u + f(u), (x, y, z) ∈ R3, t > 0, u|t=0= φ(x, y, z), (x, y, z) ∈ R3 The main result is divided into two chapters． Firstly,we study more about the stability of the three dimensional pyramid wave. By using the squeezing technique combined with the comparison principle, we not only show that such a three-dimensional pyramid wave of Allen-Cahn equation has a global exponential asymptotic stability, but also give their clear asymptotic propagation velocity. Secondly, we further generalize the existing three dimensional pyramid wave, which obtain a general pyramid wave in the three-dimensional space and prove that this generalized pyramid wave is existence in the general case. It will make the classiﬁcation of traveling wave solutions, especially in high-dimensional space, to get a new step. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224680 Collection 数学与统计学院 Recommended CitationGB/T 7714 韩帮胜. 双稳型Allen-Cahn方程的棱锥波和广义棱锥波[D]. 兰州. 兰州大学,2013.
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