請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8646完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全 | |
| dc.contributor.author | Yuan-Ting Chang | en |
| dc.contributor.author | 張菀庭 | zh_TW |
| dc.date.accessioned | 2021-05-20T19:59:14Z | - |
| dc.date.available | 2012-06-28 | |
| dc.date.available | 2021-05-20T19:59:14Z | - |
| dc.date.copyright | 2010-06-28 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-06-22 | |
| dc.identifier.citation | [1] X.F. Chen. Generation, propagation, and annihilation of metstable patterns. J.
Di erential Equations, 206:399 437, 2004. [2] X.F. Chen, J.S. Guo, F. Hamel, and H. Ninomiya. Traveling waves with paraboloid like interfaces for balanced bistable dynamics. Proc. Roy. Soc. Edinburgh Sect. A, 136(6):1207 1237, 2006. [3] X.F. Chen, J.S. Guo, F. Hamel, H. Ninomiya, and J.M. Roquejo re. Traveling waves with paraboloid like interfaces for balanced bistable dynamics. Ann. Inst. H. Poincare Anal. Non Lineaire, 24:369 393, 2007. [4] F. Hamel, R. Monneau, and J.M. Roquejo re. Existence and qualitative properties of multidimensional conical bistable fronts. Disc. Cont. Dyn. Systems, 13:1069 1096, 2005. [5] F. Hamel, R. Monneau, and J.M. Roquejo re. Asymptotic properties and clas- si cation of bistable fronts with lipschitz level sets. Disc. Cont. Dyn. Systems, 14:75 92, 2006. [6] Y. Morita and H. Ninomiya. Monostable-type traveling waves of bistable reaction- di usion equations in the multi-dimensional space. Bull. Inst. Math. Acad. Sin. (N.S.), 3:567 584, 2008. [7] H. Ninomiya and M. Taniguchi. Existence and global stability of traveling curved fronts in the allen-caha equations. J. Di erential Equations, 213:204 233, 2005. [8] H. Ninomiya and M. Taniguchi. Global stability of traveling curved fronts in the allen-caha equations. Disc. Cont. Dyn. Systems, 15:819 832, 2006. [9] M. Taniguchi. Traveling fronts of pyramidal shapes in the allen-chan equations. SIAM J. Math. Anal., 39:319 344, 2007. [10] M. Taniguchi. The uniqueness and asymptotic stability of pyramidal traveling fronts in the allen-cahn equations. J. Di erential Equations, 246:2103 2130, 2009. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8646 | - |
| dc.description.abstract | 這篇論文主要處理的問題是反應擴散方程的傳動波ut=△u+uzz-f(u)，其中(x, z)∈Rn+1是空間變數。假定f(u)是一個双雙穩定的非線性項，我們分別考慮平衡的狀態及非平衡的狀態。在平衡的狀態下，我們將描述多種連接兩個平衡點的傳動波，這些傳動波各有各的形狀。在非平衡的狀態下，我們將傳動波解限制為柱狀對稱的形式，接著證明這樣的解在n≥2時其形狀會近似於拋物面，而在n=1時會近似於超餘弦函數。除此之外，我們也將證明單穩傳動波的存在性。本篇論文的主要參考文獻的作者有以下幾位：Y. Morita、H. Ninomiya、X.F. Chen、J-S Guo、F. Hamel及J-M Roquejoffre。 | zh_TW |
| dc.description.abstract | We are dealing with traveling wave solutions of a reaction-diffusion equation ut=△u+uzz-f(u), where (x, z)=(x1,---, xn, z) ∈Rn+1 is the space variable and △ is the Laplacian in Rn. Assume that f(u) is a bistable nonlinear, then we consider the balanced case and unbalanced case respectively. In the preceding case, we describe some types of traveling waves connecting two stable equilibria. In the case of latter, we want to find out the bistable-type traveling waves with the interfaces other than plane. If the solution is restricted to be cylindrically symmetric, then we can show that the interface is asymptotically a paraboloid as n≥2 and a hyperbolic cosine curve as n=1. Besides, we prove the existence of the monostable-type traveling waves. The main references of this thesis are Y. Morita, H. Ninomiya, X.F. Chen, J-S GUO, F. Hamel and J-M Roquejoffre. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T19:59:14Z (GMT). No. of bitstreams: 1 ntu-99-R96221023-1.pdf: 3518861 bytes, checksum: 2007da03a5df732c8d4128d9e9accb30 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 口試委員會審定書....................................................i
摘要................................................................ii Abstract............................................................iii Chapter 1 Introduction..............................................1 Chapter 2 Bistable-Type Traveling Waves in the Unbalanced Condition.4 2.1 Solutions with Conical Interfaces in Multi-Dimension............5 2.2 Solutions with Pyramidal Interfaces in 3-Dimension..............7 Chapter 3 Bistable-Type Traveling Waves in the Balanced Condition...12 3.1 Preliminary.....................................................14 3.2 The Existence of Cylindrically Symmetric Traveling Waves........18 3.2.1 Approximation by Traveling Waves of Unbalanced Potentials.....18 3.2.2 Approximation by Energy Minimizers............................26 3.3 The Behavior of the Interfaces..................................31 Chapter 4 Monostable-Type Traveling Waves...........................33 4.1 The Existence of Nonplanar Traveling Waves......................35 4.1.1 A Subsolution and a Supersolution.............................37 4.1.2 Proof of Theorem 4.2. (i).....................................40 4.1.3 Proof of Theorem 4.2. (ii)....................................44 4.2 Proof of Theorem 4.1............................................46 Bibliography........................................................49 | |
| dc.language.iso | en | |
| dc.title | 反應擴散方程的非平面傳動波 | zh_TW |
| dc.title | Nonplanar Traveling Wave Solutions of Reaction-Diffusion Equations | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 夏俊雄,林太家 | |
| dc.subject.keyword | 傳動波,反應擴散方程,雙穩定的非線性項,界面,雙穩,單穩, | zh_TW |
| dc.subject.keyword | traveling wave,reaction-diffusion equation,bistable nonlinearity,interface,bistable,monostable, | en |
| dc.relation.page | 50 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2010-06-23 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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