簡易檢索 / 詳目顯示

研究生: 吳昌鴻
Chang-Hong Wu
論文名稱: Existence and Uniqueness of Traveling Waves for a Monostable 2-D Lattice Dynamical System
指導教授: 郭忠勝
Guo, Jong-Shenq
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2007
畢業學年度: 95
語文別: 英文
論文頁數: 19
中文關鍵詞: 格子動態系統單穩定型行進波波速波形
英文關鍵詞: Lattice dynamical system, monostable, traveling wave, wave speed, wave profile
論文種類: 學術論文
相關次數: 點閱:202下載:5
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 我們研究二維度的單穩定型格子動態系統的行進波。首先我們證明存在一個最小的速度使得行進波存在的充分必要條件是行進波的速度大於或等於此最小的速度。然後我們證明給定一個速度後,在不考慮平移的情況下,行進波的波形是唯一的。更進一步的,我們知道行進波的波形是嚴格單調的。

    We study traveling waves for a two-dimensional lattice dynamical system with monostable nonlinearity. We first prove that there is a minimal speed such that a traveling wave exists if and only if its speed is above this minimal speed. Then we show the uniqueness (up to translations) of wave profile for each given speed. Moreover, any wave profile is strictly monotone.

    1.Introduction ..............................1 2.Preliminaries .............................3 3.Existence .................................5 4.Uniqueness ................................9

    [1] J.W. Cahn, J. Mallet-Paret, E.S. van Vleck, Traveling wave solutions for systems of ODEs on a twodimensional
    spatial lattice, SIAM J. Appl. Math. 59 (1998), 455–493.
    [2] J. Carr, A. Chmaj, Uniqueness of travelling waves for nonlocal monostable equations, Proc. Amer. Math.
    Soc. 132 (2004), 2433–2439.
    [3] P.W. Bates, X. Chen, A. Chmaj, Traveling waves of bistable dynamics on a lattice, SIAM J. Math.
    Anal. 35 (2003), 520–546.
    [4] X. Chen, J.-S. Guo, Existence and asymptotic stability of travelling waves of discrete quasilinear
    monostable equations, J. Diff. Eqns 184 (2002), 549–569.
    [5] X. Chen, J.-S. Guo, Uniqueness and existence of travelling waves for discrete quasilinear monostable
    dynamics, Math. Ann. 326 (2003), 123–146.
    [6] X. Chen, S.-C. Fu., J.-S. Guo, Uniqueness and asymptotics of traveling waves of monostable dynamics
    on lattices, SIAM J. Math. Anal. 38 (2006), 233–258.
    [7] S.-N. Chow, J. Mallet-Paret, W. Shen, Traveling waves in lattice dynamical systems, J. Diff. Eqns. 149
    (1998), 248–291.
    [8] W. Ellison, F. Ellison, Prime Numbers, A Wiley-Interscience Publication, John Wiley-Sons, NY; Hermann,
    Paris, 1985.
    [9] R.A. Fisher, The advance of advantageous genes, Ann. Eugenics 7 (1937), 355–369.
    [10] S.-C. Fu, J.-S. Guo, S.-Y Shieh, Travelling waves for some discrete quasilinear parabolic equations,
    Nonlinear Anal. TMA 48 (2002), 1137–1149.
    [11] 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. Univ. Moskov. Ser. Internat.,
    Sect. A 1 (1937), 1-25.
    [12] J. Mallet-Paret, The Fredholm alternative for functional-differential equations of mixed type, J. Dynam.
    Diff. Eqns. 11 (1999), 1–47.
    [13] J. Mallet-Paret, The global structure of traveling waves in spatially discrete dynamical systems, J. Dynam.
    Diff. Eqns. 11 (1999), 49–127.
    [14] D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, NJ, 1941.
    [15] J. Wu, X. Zou, Asymptotic and periodic boundary values problems of mixed PDEs and wave solutions
    of lattice differential equations, J. Diff. Eqns 135 (1997), 315–357.
    [16] B. Zinner, Stability of traveling wavefronts for the discrete Nagumo equations, SIAM J. Math. Anal. 22
    (1991), 1016–1020.
    [17] B. Zinner, Existence of traveling wavefronts for the discrete Nagumo equations, J. Diff. Eqns. 96 (1992),
    1–27.
    [18] B. Zinner, G. Harris, & W. Hudson, Traveling wavefronts for the discrete Fisher’s equation, J. Diff.
    Eqns. 105 (1993), 46–62.

    QR CODE