某類週期性網格型微分方程行波解之研究

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：24

、訪客IP：18.222.125.171

姓名

蘇美慈(Mei-tzu Su) 查詢紙本館藏

畢業系所

數學系

論文名稱

某類週期性網格型微分方程行波解之研究
(A Study on Traveling Wave Solutions of Some Periodic Lattice Differential Equations)

相關論文

★ 在只有部份疾病訊息狀況下,有關二元診斷篩檢法之二個概似比特徵之概似推論方法	★ 混合噪聲的即時圖像去噪在螢光顯微鏡圖像和古畫中的應用
★ 遲滯型細胞神經網路之行進波	★ 遲滯型細胞神經網絡行進波之結構
★ 網格型微分方程的行進波的數值解	★ 某類網格型微分方程行波解的存在性，唯一性及穩定性
★ 網格型動態系統行波解之研究	★ 矩陣值勢能上的sofic測度
★ 在Sofic Shift上的多重碎型分析	★ 某類傳染病模型微分方程行波解之研究
★ 某類三維癌症模型之整體穩定性分析	★ 三種競爭合作系統之行波解的存在性
★ 離散型Lotka-Volterra競爭系統之行波解的穩定性	★ On the Existence of the Stem Entropy on Markov-Cayley tree

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

在本篇論文中，我們主要研究某類diffusively function-coupled週期性網格型微分方程行波解的存在性。根據參考文獻[14]的方法，我們證明當波速高於最小波速時，行波解是存在的。此外，我們探討此類行波解的一些特性。

摘要(英)

In this thesis we investigate the existence of traveling wave solutions of some diffusively function-coupled periodic lattice differential equations. Following the ideas of [14], we show that if the wave speed is above the minimal wave speed, then traveling wave solution exists. Moreover, we discuss the properties of that traveling wave solution.

關鍵字(中)

★ 存在性
★ 週期性
★ 上解
★ 下解
★ 行波解

關鍵字(英)

★ traveling wave solutions
★ existence
★ subsolution
★ supersolution
★ monostable

論文目次

中文摘要 ……………………………………………………………i
英文摘要 ………………………………………………………… ii
Contents …………………………………………………………iii
Abstract ……………………………………………………………1
1.Introduction ……………………………………………………2
2.Existence of the solution for problem (P) ……………3
3.Properties of the traveling wave solution ……………18
References ………………………………………………………28

參考文獻

[1] H. Berestycki, F. Hamel, Front propagation in periodic excitable media, Comm. Pure Appl. Math. 55 (2002), 949-1032.
[2] H. Berestycki, F. Hamel, N. Nadirashvili, The speed of propagation for KPP type problems. I -Periodic framework, J. Europ. Math. Soc. (2005), to appear.
[3] H. Berestycki, F. Hamel, L. Roques, Analysis of the periodically fragmented environment model: I - Influence of periodic heterogeneous environment on species persistence, J. Math. Biol. (2005), to appear.
[4] H. Berestycki, F. Hamel, L. Roques, Analysis of the periodically fragmented environment model: II - Biological invasions and pulsating travelling fronts, J. Math. Pures Appl. (2005), to appear.
[5] X. Chen, J.-S. Guo, Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations, J. Differential Equations 184 (2002), 549-569.
[6] X. Chen, J.-S. Guo, Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics, Math. Ann. 326 (2003), 123-146.
[7] S.N. Chow, J. Mallet-Paret, W. Shen, Travelling waves in lattice dynamical systems, J. Differential Equations 149 (1998), 249-291.
[8] T. Erneux, G. Nicolis, Propagation waves in discrete bistable reactiondiffusion systems, Physica D 67 (1993), 237-244.
[9] G. F´ath, Propagation failure of traveling waves in a discrete bistable medium, Physica D 116 (1998), 176-190.
[10] P.C. Fife, Mathematical aspects of reacting and diffusing systems, Lecture Notes in Biomathematics 28, Springer Verlag, 1979.
[11] R.A. Fisher, The advance of advantageous genes, Ann. Eugenics 7 (1937), 335-369.
[12] M.I. Freidlin, Limit theorems for large deviations and reaction-diffusion equations, Ann. Probab. 13 (1985), 639-675.
[13] J. Gartner, M.I. Freidlin, On the propagation of concentration waves in periodic and random media, Soviet Math. Dokl. 20 (1979), 1282-1286.
[14] J.-S. Guo and F. Hamel, Front propogation for discrete periodic monostable equations, Math. Ann. 335 (2006), 489-525.
[15] R. A. Horn, C. R. Johnson, Matrix analysis, Cambridge University Press, 1985.
[16] C.-H. Hsu, S.-S. Lin, Existence and multiplicity of traveling waves in a lattice dynamical system, J. Differential Equations 164 (2000), 431-450.
[17] W. Hudson, B. Zinner, Existence of traveling waves for a generalized discrete Fisher’s equation, Comm. Appl. Nonlinear Anal. 1 (1994), 23-46.
[18] W. Hudson, B. Zinner, Existence of travelling waves for reaction-dissusion equations of Fisher typein periodic media, In: Boundary Value Problems for Functional Differential Equations, J. Henderson (ed.), World Scientific, 1995, pp. 187-199.
[19] J.P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math. 47 (1987), 556-572.
[20] A.N. Kolmogorov, I.G. Petrovsky, N.S. 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, Bull. Universit´e d’´Etat `a Moscou, Ser. Int., Sect. A. 1 (1937), 1-25.
[21] J. Mallet-Paret, The Fredholm alternative for functional differential equations of mixed type, J. Dyn. Differential Equations 11 (1999), 1-48.
[22] J. Mallet-Paret, The global structure of traveling waves in spatial discrete dynamical systems, J. Dyn. Differential Equations 11 (1999), 49-127.
[23] N. Shigesada, K. Kawasaki, Biological invasions: theory and practice, Oxford Series in Ecology and Evolution, Oxford, Oxford University Press, 1997.
[24] N. Shigesada, K. Kawasaki, E. Teramoto, Traveling periodic waves in heterogeneous environments, Theor. Popul. Biology 30 (1986), 143-160.
[25] B. Shorrocks, I.R. Swingland, Living in a Patch Environment, Oxford University Press, New York, 1990.
[26] J. Smoller, Shock waves and reaction diffusion equations. Springer-Verlag, Berlin, New York, 1983.
[27] J. Wu, X. Zou, Asymptotical and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, J. Differential Equations 135 (1997), 315-357.
[28] X. Xin, Existence and stability of travelling waves in periodic media governed by a bistable nonlinearity, J. Dynamics Diff. Equations 3 (1991), 541-573.
[29] X. Xin, Existence of planar flame fronts in convective-diffusive periodic media, Arch. Rational Mech. Anal. 121 (1992), 205-233.
[30] X. Xin, Existence and nonexistence of traveling waves and reactiondiffusion front propagation in periodic media, J. Stat. Physics 73 (1993), 893-925.
[31] J.X. Xin, Existence of multidimensional traveling waves in tranport of reactive solutes through periodic porous media, Arch. Rational Mech. Anal. 128 (1994), 75-103.
[32] J. Xin, Front propagation in heterogeneous media, SIAM Review 42 (2000), 161-230.
[33] H.F. Weinberger, On spreading speeds and traveling waves for growth and migration in periodic habitat, J. Math. Biol. 45 (2002), 511-548.
[34] B. Zinner, Existence of traveling wavefront solutions for the discrete Nagumo equation, J. Differential Equations 96 (1992), 1-27.
[35] B. Zinner, G. Harris, W. Hudson, Traveling wavefronts for the discrete Fisher’s equation, J. Differential Equations 105 (1993), 46-62.

指導教授

許正雄(Cheng-hsiung Hsu)

審核日期

2008-6-25

推文