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研究生:黃介民
研究生(外文):HUANG, JIE-MIN
論文名稱:某離散模型中穩態波之探討
論文名稱(外文):A Study of Stationary Waves for Some Discrete Model
指導教授:吳昌鴻
指導教授(外文):WU, CHANG HONG
口試委員:葉宗鑫張覺心
口試委員(外文):YEH, TZUNG SHINCHANG, CHUEH-HSIN
口試日期:2017-05-22
學位類別:碩士
校院名稱:國立臺南大學
系所名稱:應用數學系碩士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:英文
論文頁數:22
中文關鍵詞:空間離散模型行進波穩態波投射法
外文關鍵詞:Spatially discrete modeltraveling wavesstationary wavesshooting argument approach
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本論文探討一個用無限維動態系統所描述的離散模型中之穩態波存在性。所謂的穩態波意指傳播速度為零的行進波。在某些適當的條件下,我們運用投射法(打靶法)來證明單調穩態波的存在性。
In this thesis, we investigate the existence of stationary waves for a spatially discrete model described by infinite-dimensional dynamical systems. By a stationary wave solution, we mean a traveling wave solution with zero speed of propagation. Under certain suitable conditions, we use a shooting argument approach to show the existence of monotone stationary waves.
致謝.................................i
中文摘要.............................ii
英文摘要.............................iii
目次.................................iV

1.Introduction.......................1
2.Main Result........................4
3.Conclusion.........................13
References...........................13
[1] D.G. Aronson, H.F. Weinberger,Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in Partial Differential Equations and Related Topics, Lecture Notes in Math., Vol.446, Springer, Berlin, 1975, 5-49.
[2] J. Bell, C. Cosner, Threshold behavior and propagation for nonlinear differentia-difference systems motivated by modeling myelinated axons. Quart. J. Appl. Math. 42 (1984), 1-14.
[3] A. Carpio, S. J. Chapman, S. Hastings and J. B. McLeod, Wave Solution for a Dicrete Reaction-diffusion Equation, Euro. Jnl of Applied Mathematics. 11 (2000), 399-412.
[4] J.D. Murray, Mathematical Biology, 3rd ed. Springer, Berlin, (1993).
[5] R. A. Fisher, The wave of advance of advantageous genes, Ann. Eug., 7 (1937), pp. 355-369.
[6] J. Frenkel, T. Kontorova, On the theory of plastic deformation and twinning, J. Phys. USSR 13 (1938), 1-10.
[7] K. P. Hadeler, F. Rothe, Travelling fronts in nonlinear diffusion equations, J. Math. Biol., 2 (1975), 251-263.
[8] J.P, Keener, Propagation and its failure in coupled systems of discrete excitable cells. SIAM J. Appl. Math. 47 (1987), 556-572
[9] A. Kolmogorov, I. Petrovsky and N. Piscounov, Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem, Bull. State Univ. Mos., (1937).
[10] B. Zinner, Existence of traveling wavefront solutions for the discrete Nagumo equation. J. Diff. Eq.96 (1992), 1-27.
[11] B. Zinner, Stability of traveling wavefronts for the discrete Nagumo equation. SIAM J. Math. Anal. 22 (1991), 1096-1020.
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