在这篇论文中，我们考虑二维中的Gray-Scott 模型核心问题的解: / [ 附圖]. / 对于足够小的ε，我们会构造一个“多个凸 的解。这些解的“凸 会分布在一个正多边形的顶点上。在这个解的U 方向上，经过一个合适的放缩之后，它会看起来像下列方程的唯一对称解： / [ 附圖]. / 此外，我们同时也会构造单个“凸 和两个“凸 的解。 / In this thesis, we consider solutions to the core problem for Gray-Scott model in R²: / [With mathematic formula]. / We construct multi-bump solutions for this problem for all sufficiently small ε. The centers of these bumps are located at the vertices of a regular polygon, andthey resemble, after a suitable scaling in their U-coordinate, the unique radial solution of / [With mathematic formula]. / The solutions with one single bump and two bumps are also constructed. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Yip, Chit Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 45-46). / Abstracts also in Chinese. / Chapter 1 --- Introduction: Derivation of the Core Problem --- p.6 / Chapter 2 --- One-dimensional core problem --- p.12 / Chapter 3 --- Main results on two-dimensional core problem --- p.19 / Chapter 4 --- Proof of Theorem 3.1 --- p.22 / Chapter 4.1 --- Estimate for S₁({U+03A6}) --- p.24 / Chapter 4.2 --- Estimate for N₁({U+03A6}) --- p.25 / Chapter 4.3 --- Estimate for S₁({U+03A6}₁) - S₁({U+03A6}₂) --- p.26 / Chapter 4.4 --- Estimate for N₁({U+03A6}₁) - N₁({U+03A6}₂) --- p.26 / Chapter 5 --- Proof of Theorem 3.2 --- p.29 / Chapter 5.1 --- Estimate for S₂({U+03A6}) --- p.33 / Chapter 5.2 --- Estimate for N₂({U+03A6}) --- p.34 / Chapter 5.3 --- Estimate for S₂({U+03A6}₁) - S₂({U+03A6}₂) --- p.34 / Chapter 5.4 --- Estimate for N₂({U+03A6}₁) - N₂({U+03A6}₂) --- p.35 / Chapter 5.5 --- The reduced problem --- p.35 / Chapter 6 --- Proof of Theorem 3.3 --- p.40 / Chapter 6.1 --- Invariance under permutations --- p.41 / Chapter 6.2 --- Reducing number of equations for regular polygons --- p.42 / Bibliography --- p.45
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328422 |
| Date | January 2012 |
| Contributors | Yip, Chit Ming., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (46 leaves) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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