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研究生: 李宜展
論文名稱: 自動催化反應擴散系統的行進波
Traveling Waves of Autocatalytic Reaction-Diffusion Systems
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: 2008
畢業學年度: 96
語文別: 英文
論文頁數: 13
中文關鍵詞: 自動催化行進波最小波速反應擴散
英文關鍵詞: autocatalysis, traveling wave, minimum speed, reaction-diffusion
論文種類: 學術論文
相關次數: 點閱:130下載:2
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  • 這篇論文主要是對於行進波在等溫化學反應 A + nB ->(n+1)B (其中A是反應物,B是自動催化劑)的發展作一個概括性的介紹。存在一個最小波速使得行進波解存在的充分必要條件為其波速大於或等於此一最小波速。我們將討論早期研究對於此最小波速的估計。

    1. Introduction 3 2. The extreme cases 4 3. General properties of traveling wave solutions 5 4. Quadratic autocatalysis, n=1 6 5. The existence of v_min when n>1 7 6. The estimate of v_min when n>1 8

    [1]
    D. G. Aronson and H. F. Weinberger,Multidimensional diffusion arising in population genetics,Adv. Math. 30(1978)
    ,33-76.

    [2]
    N. J. T. Bailey, The mathematical theory of infectious diseases, Griffen,London,(1975).

    [3]
    J. Billingam and D.J. Needham, The development of traveling
    wave in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form traveling waves, Phil.
    Trans. Roc. Soc. A 334 (1991), 1-24.

    [4]
    J. Billingam and D. J. Needham, The development of traveling wave in quadratic and cubic autocatalysis with
    unequal diffusion rates. II. An initial value problem with
    immobilized or nearly immobilized autocatalyst, Phil. Trans. Roc. Soc. A 336 (1991), 497-539.

    [5]
    X. Chen and J.-S. Guo, Existence and asymptotic stability
    of traveling waves of discrete quasilinear monostable equations, J. Differential Equations 184 (2) (2002),
    549-569.

    [6]
    X. Chen and Y. W. Qi, Sharp estimates on minimum traveling
    wave speed of reaction diffusion systems modelling autocatalysis, SIAM J. Math. Anal. 39 (2007), no. 2, 437-448.

    [7]
    P. C. Fife and J. B. McLeod, The approach of nonlinear diffusion equations to traveling wave front solutions, Arch. Ration. Mech. Anal. 65 (1977), 335-361.

    [8]
    Y. Hosono, Phase plane analysis of traveling waves for higher order autocatalytic reaction-diffusion systems,
    Discrete Contin. Dyn. Syst. Ser. B, 8 (2007), 115-125.

    [9]
    Y. Hosono, Propagation speeds of traveling fronts for higher order autocatalytic reaction-diffusion systems,
    Japan J. Indust. Appl. Math. 24, (2007), 79-104. 12

    [10]
    J. H. Merkin and D. J. Needham, Propagating reaction-diffusion waves in a simple isothermal quadratic autocatalytic chemical systems, J. Eng. Math. 23 (1989)
    , 343-356.

    [11]
    J. H. Merkin and D. J. Needham, The development of traveling waves in a simple isothermal chemical II. Cubic
    autocatalysis with quadratic and linear decay, Proc. Roy.
    Soc. London A, 430 (1990), 315-345.

    [12]
    J. H. Merkin and D. J. Needham, The development of traveling waves in a simple isothermal chemical IV. Cubic
    autocatalysis with quadratic and linear decay, Proc. Roy.
    Soc. London A, 434 (1991), 531-554.

    [13]
    Y.W.Qi,The development of traveling waves in cubic auto-catalysis with different rates of diffusion, Physica D
    226 (2007), 129-135.
    [14]
    D. Sattinger, On the stability of waves of nonlinear parabolic systems, Adv. Math. 22 (1976), 312-355.

    [15]
    H. Takase and B. D. Sleeman, Traveling wave solutions
    to monostable reaction-diffusion systems of mixed monotone
    type, Proc. Roy. Soc. Lond. A, 455 (1999), 1561-1598.

    [16]
    J. Xin, Front propagation in heterogeneous media, SIAM Rev.
    42 (2000), 161-230. 13

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