請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/36567
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
dc.contributor.author | Hui-Ying Chuang Wu | en |
dc.contributor.author | 莊吳慧瑩 | zh_TW |
dc.date.accessioned | 2021-06-13T08:05:52Z | - |
dc.date.available | 2006-07-27 | |
dc.date.copyright | 2005-07-27 | |
dc.date.issued | 2005 | |
dc.date.submitted | 2005-07-21 | |
dc.identifier.citation | [1]Alison L. Kay, Jonathan A. Sherratt and J. B.
Mcleod.Comparison theorems and variable speed waves for a scalar reaction-diffusion equation.Proceedings of the Royal Society of Edinburgh,131A, 1131-1161, 2001. [2]P. C. Fife and J. B. Mcleod. The approach of solutions of nonlinear diffusion equations to travelling front solutions.Arch.Ration.Mech.Analysis 65(1977),335-361. [3]P. C. Fife and J. B. Mcleod. A phase plane discussion of convergence to travelling fronts for nonlinear diffusion.Arch.Ration.Mech.Analysis 75(1981),281-314. [4]D. J. Needham and A. N. Barnes. Reaction-diffusion and phase waves occuring in a class of scalar reaction- diffusion equations.Nonlinearity 12(1911),41-58. [5]J. A. Sherratt and B. P. Marchant. Algebraic decay and variable speeds in wavefront solutions of a scalar reaction-diffusion equation.IMA J. Apple Math 56 (1996),289-302. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/36567 | - |
dc.description.abstract | 常係數反應擴散方程的波型解長久以來已被廣泛地研究。Kolmogorov-Fisher型態的方程式有兩種基本型式,其中一種是非線性項有唯一零解的,另一種是非線性項有較高階零解的。這篇論文是在討論方程式u_t=u_{xx}+f(u), x is in (-infty, infty)
的解,當f(u)={e^{-1/u}}*(1-u), f(1)=0, f'(1)< 0 所採用的方法是利用單調性取u,t作為自變數,p(u,t)=u_x(x,t)作為應變數,並對p方程運用下解及上解之概念。 | zh_TW |
dc.description.abstract | Wavefront solutions of scalar reaction-diffusion equations have been intensively studied for many years. There are two basic cases for the Kolmogorov-Fisher type equations, typified by a nonlinear term with simple zero root and a nonlinear term with higher order zero root. The paper is concerned with solutions u(x,t) of the equation
u_t=u_{xx}+f(u), x is in (-infty, infty) in the case f(u)={e^{-1/u}}*(1-u), f(1)=0, f'(1)< 0 The approach is to use the monotonicity to take u and t as independent variables and p(u,t)=u_x(x,t) as the dependent variable, and to apply ideas of sub- and super-solutions to the diffusion equation for p. | en |
dc.description.provenance | Made available in DSpace on 2021-06-13T08:05:52Z (GMT). No. of bitstreams: 1 ntu-94-R90221021-1.pdf: 364078 bytes, checksum: ae7b9d97752bedd768d839f328e696b9 (MD5) Previous issue date: 2005 | en |
dc.description.tableofcontents | 1. Introduction... 1~5
1.1. Background 1.2. The numerical results from four different kinds of initial conditions 1.3. P-equation 1.4. Sub- and super-solutions 1.5. Comparison theorem for the p-equation 2. Exponentially decaying initial conditions...5~6 2.1. Sub-solution 2.2. Super-solution 2.3. Conclusion 3. Algebraically decaying initial conditions,alpha=1...6~14 3.1. Sub-solution for a> c_{crit} 3.2. Super-solution for a> c_{crit} 3.3. Conclusion 4. Algebraically decaying initial conditions,alpha>1...14~15 4.1. Sub-solution 4.2. Super-solution 4.3. Conclusion 5. Algebraically decaying initial conditions,alpha<1...15~17 5.1. Sub-solution 5.2. Super-solution 5.3. Initial conditions Phi not covered by the super- solution overline{Psi} 5.4. Conclusion 6. Problem...18~21 6.1. Sub-solution 6.2. Super-solution 6.3. Conclusion | |
dc.language.iso | zh-TW | |
dc.title | Kolmogorov-Fisher 型態的反應擴散方程 | zh_TW |
dc.title | Reaction-Diffusion Equations of the Kolmogorov-Fisher Type | en |
dc.type | Thesis | |
dc.date.schoolyear | 93-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 林太家(Tai-Chia Lin),陳建隆(Jann-Long Chern) | |
dc.subject.keyword | 反應擴散方程, | zh_TW |
dc.subject.keyword | Kolmogorov-Fisher Type, | en |
dc.relation.page | 22 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2005-07-21 | |
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 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-94-1.pdf 目前未授權公開取用 | 355.54 kB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。