研究生: |
謝升耀 Shang-Yau Shieh |
---|---|
論文名稱: |
離散的費雪類方程其旅行波解的存在性 Existence of traveling wavefronts for the discrete Fisher's type equation |
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: | 1999 |
畢業學年度: | 87 |
語文別: | 英文 |
論文頁數: | 11 |
中文關鍵詞: | 離散費雪方程 、旅行波 |
英文關鍵詞: | discrete Fisher's equation, traveling wavefront |
論文種類: | 學術論文 |
相關次數: | 點閱:356 下載:0 |
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 |
我們討論無限的非線性微分方程組,此方程組稱為離散的費雪類方程。
當常數d在某些限制範圍之下,我們得到此系統旅行波解的存在性。
We study the infinite system of coupled nonlinear differential equations which is called the discrete Fisher's type equation.
Under the assumption that the coupled constant is not strong enough, we obtain the existence of traveling wavefronts for this system.
[1]. H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, Siam Rev. 18, No. 4 (1976).
[2]. H. Amann and S. A. Weiss, On the uniqueness of the topological degree, Math. Z. 130 (1973), 39-45.
[3]. D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion and nerve propagation, Lecture Notes in Math. 446(1981), 5-49.
[4]. J. Bell, Some threshold results for models of myelinated nerves, Math. Biosci. 4 (1981),181-190.
[5]. J. Bell and C. Cosner, Threshold behavior and propagation for nonlinear differential-difference systems notivated by modeling myelinated axons, Quart. Appl. Math. 42 (1984), 1-14.
[6]. R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics 7 (1937), 355-369.
[7]. R. FitzHugh, Impulse and physiological states in models of nerve membrane, Biophys. J. 1 (1961), 445-466.
[8]. D. Hankerson and B. Zinner, Wavefronts for a cooperative tridiagonal system of differential equations, J. Dynamics Differential Equations 5 (1993), 359-373.
[9]. J. P. Keener, Propagation and its failure in the discrete Nagumo equation, in Proc. Conference on Ordinary and Partial Differential Equations, Dundee, Scotland (1986), 95-112.
[10]. J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math. 47 (1987), 556-572.
[11]. J. Nagumo, S. Ariomot. And S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE 50 (1962), 2061-2070.
[12]. A. c. Scott, Active and Nonlinear Wave Propagation in Electronics, Wiley-Interscience, New York (1970).
[13]. B. Zinner, Existence of traveling wavefront solutions for the discrete Nagumo equation, J. Differential Equations 96 (1992), 1-27.
[14]. B. Zinner, Stability of traveling wavefronts for the discrete Nagumo equation, SIAM J. Math. Anal. 22 (1991), 1016-1020.
[15]. B. Zinner, G. Harris, and W. Hudson, Traveling wavefronts for the discrete Fisher's equation, Journal of Differential Equations 105 (1993), 46-62.