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題名 離散型反應擴散方程的全解
Entire Solutions for Discrete Reaction-Diffusion Equations
作者 王宏嘉
Wang,Hong-Jia
貢獻者 符聖珍
王宏嘉
Wang,Hong-Jia
關鍵詞 離散型反應擴散方程
全解
discrete reaction-diffusion equation
entire solution
日期 2006
上傳時間 17-Sep-2009 13:46:37 (UTC+8)
摘要 這篇文章中，我們探討離散型反應擴散方程u_t(x,t)=u(x+1,t)-2u(x,t)+u(x-1,t)+f(u(x,t))，其中
反應項f(u)=u^2(1-u)。在此，
我們證明此方程式存在一種全解其動態行為宛如兩個來自x軸兩端相向而行的行波。
This paper deals with a discrete reaction-diffusion equation
u_t(x,t)=u(x+1,t)-2u(x,t)+u(x-1,t)+f(u(x,t)),
where f(u)=u^2(1-u). Here, we prove there exist entire solutions which behave as two
traveling waves coming from both sides of x-axis.
參考文獻 [1] X. Chen and J.-S. Guo, Existence and asymptotic stability of traveling waves
of discrete quasilinear monostable equations, Journal of Differential Equations
184 (2002), 549-569.
[2] X. Chen and J.-S. Guo, Uniqueness and existence of traveling waves for discrete
quasilinear monostable dynamics, Mathematische Annalen 326 (2003), 123-146.
[3] X. Chen, S.-C. Fu and J.-S. Guo, Uniqueness and asymptotics of traveling waves
of monostable dynamics on lattices, SIAM Journal on Mathematical Analysis
38 (2006), 233-258.
[4] R.A Fisher, The advance of adavantageous genes, Annals Eugenics 7 (1937),
355-369.
[5] J.-S. Guo and Y. Morita, Entire solutions of reaction-diffusion equations and an
application to discrete diffusive equations, Discrete and Continuous Dynamical
Systems 12 (2005), 193-212.
[6] A. Kolmogorov, I. Petrovsky, and N. Piskunov, Etude de l’´equation de la diffusion
avec croissance de la quantit´e de mati´ere et son application ´a un probl´eme
biologique, Bulletin Universite d’Etat a Moscow Series Internationale Section
A 1 (1937), 1-26.
描述 碩士
國立政治大學
應用數學研究所
93751002
95
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0093751002
資料類型 thesis
dc.contributor.advisor 符聖珍zh_TW
dc.contributor.author (Authors) 王宏嘉zh_TW
dc.contributor.author (Authors) Wang,Hong-Jiaen_US
dc.creator (作者) 王宏嘉zh_TW
dc.creator (作者) Wang,Hong-Jiaen_US
dc.date (日期) 2006en_US
dc.date.accessioned 17-Sep-2009 13:46:37 (UTC+8)-
dc.date.available 17-Sep-2009 13:46:37 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 13:46:37 (UTC+8)-
dc.identifier (Other Identifiers) G0093751002en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32574-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 93751002zh_TW
dc.description (描述) 95zh_TW
dc.description.abstract (摘要) 這篇文章中，我們探討離散型反應擴散方程u_t(x,t)=u(x+1,t)-2u(x,t)+u(x-1,t)+f(u(x,t))，其中
反應項f(u)=u^2(1-u)。在此，
我們證明此方程式存在一種全解其動態行為宛如兩個來自x軸兩端相向而行的行波。		zh_TW
dc.description.abstract (摘要) This paper deals with a discrete reaction-diffusion equation
u_t(x,t)=u(x+1,t)-2u(x,t)+u(x-1,t)+f(u(x,t)),
where f(u)=u^2(1-u). Here, we prove there exist entire solutions which behave as two
traveling waves coming from both sides of x-axis.		en_US
dc.description.tableofcontents Contents
Abstract i
中文摘要 ii
1 Introduction . . . . . . . . . . . . . . . . . . . . . .1
2 Entire solutions for discrete reaction-diffusion equations. . . . . . . . . . . . . . . . . . . . . .4
2.1 Preliminaries. . . . . . . . . . . . . . . . . . . . . .4
2.2 Existence of entire solutions. . . . . . . . . . . . . . . . . . . . . .5
References. . . . . . . . . . . . . . . . . . . . . .14		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0093751002en_US
dc.subject (關鍵詞) 離散型反應擴散方程zh_TW
dc.subject (關鍵詞) 全解zh_TW
dc.subject (關鍵詞) discrete reaction-diffusion equationen_US
dc.subject (關鍵詞) entire solutionen_US
dc.title (題名) 離散型反應擴散方程的全解zh_TW
dc.title (題名) Entire Solutions for Discrete Reaction-Diffusion Equationsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] X. Chen and J.-S. Guo, Existence and asymptotic stability of traveling waveszh_TW
dc.relation.reference (參考文獻) of discrete quasilinear monostable equations, Journal of Differential Equationszh_TW
dc.relation.reference (參考文獻) 184 (2002), 549-569.zh_TW
dc.relation.reference (參考文獻) [2] X. Chen and J.-S. Guo, Uniqueness and existence of traveling waves for discretezh_TW
dc.relation.reference (參考文獻) quasilinear monostable dynamics, Mathematische Annalen 326 (2003), 123-146.zh_TW
dc.relation.reference (參考文獻) [3] X. Chen, S.-C. Fu and J.-S. Guo, Uniqueness and asymptotics of traveling waveszh_TW
dc.relation.reference (參考文獻) of monostable dynamics on lattices, SIAM Journal on Mathematical Analysiszh_TW
dc.relation.reference (參考文獻) 38 (2006), 233-258.zh_TW
dc.relation.reference (參考文獻) [4] R.A Fisher, The advance of adavantageous genes, Annals Eugenics 7 (1937),zh_TW
dc.relation.reference (參考文獻) 355-369.zh_TW
dc.relation.reference (參考文獻) [5] J.-S. Guo and Y. Morita, Entire solutions of reaction-diffusion equations and anzh_TW
dc.relation.reference (參考文獻) application to discrete diffusive equations, Discrete and Continuous Dynamicalzh_TW
dc.relation.reference (參考文獻) Systems 12 (2005), 193-212.zh_TW
dc.relation.reference (參考文獻) [6] A. Kolmogorov, I. Petrovsky, and N. Piskunov, Etude de l’´equation de la diffusionzh_TW
dc.relation.reference (參考文獻) avec croissance de la quantit´e de mati´ere et son application ´a un probl´emezh_TW
dc.relation.reference (參考文獻) biologique, Bulletin Universite d’Etat a Moscow Series Internationale Sectionzh_TW
dc.relation.reference (參考文獻) A 1 (1937), 1-26.zh_TW