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姓名 郭權緻(Chuan-chih Kuo)  查詢紙本館藏   畢業系所 數學系
論文名稱 某類傳染病模型微分方程行波解之研究
(Traveling Wave Solutions for Some EpidemicModels)
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摘要(中) 在本篇論文中,我們主要研究某類傳染病模型的微分方程,其行波解的存
在且該行波解為monotonic。利用monotone iteration這個方法,結合我們所
建構的上解和下解,證明當存在最小的波速c* ,而且當波速高於最小波速
c* 時,行波解是存在的。
摘要(英) The purpose of this thesis is to investigate the existence of monotonic traveling
wave solutions for some epidemic models. Using the monotone iteration method,
combining with a pair of upper solution and lower solution, we show that there
exist a minimal wave speed c* such that if the wave speed is greater than c* ,
then there exist monotone traveling wave solutions.
關鍵字(中) ★ monotone iterations
★ 上解
★ 下解
★ 行進波
★ 傳染病模型
關鍵字(英) ★ upper and lower
★ traveling wave
★ epidemic model
論文目次 中文摘要........................................................................................................i
英文摘要.......................................................................................................ii
Contents.......................................................................................................iii
Abstract.........................................................................................................1
1. Introduction...............................................................................................2
2. Local Analysis and Minimal Wave Speed............................................5
3. Solution Operator and Its Properties.........................................................8
4. Construction of Upper and Lower Solutions...........................................10
5. Proof of the Main Theorem.....................................................................14
References...................................................................................................17
參考文獻 [1] D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population
genetics, combustion, and nerve pulse propagtion, in partial differential
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[2] V. Capasso, Mathematical structures of epidemic systems, Lecture
Notes in Biomath. 97, Springer-Verlag, Heidelberg,1993.
[3] V. Capasso and K. Kunisch, A reaction-diffusion system arising in
modelling man-environment diseases, Quart. Appl. Math. 46 (1988),
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[4] E. A. Coddington and N. Levinson, Theory of Ordinary Differential
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[5] V. Capasso and S. L. Paveri-Fontana, A mathmatical model for the
1973 cholera epidemic in the European Mediterranean region, Revue
d’Epidemiol. etde Sant’e Publique 27 (1979), 121-132
[6] V. Capsso and R. E. Wilson, Analysis of reaction-diffusion system
modeling man-environment-man epidemics,SIAM. J. Appl. Math. 57
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[7] O. Diekmann, Thresholds and traveing waves for the geographical
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[8] P. C. Fife, Mathematical Aspects of Reacting and Diffusing System,
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[10] K. P. Hadeler, Nonlinear propagation in reaction transport systems,
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[12] J. D. Murray, Mathematical Biology, Springer-verlag, New York, 1989.
[13] S. Ma, Travelling wavefronts for delayed reaction-diffusion systems via
a fixed point theorem, J. Diff. Eqns., 171 (2001), 251-263.
[14] K. W. Schaaf, Asymptotic behavior and traveling waves aolutions for
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waves in delayed reaction-diffusion eqautions, SIAM J. Math. Anal.,31
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Waves Solutions of Parabolic Systems, Translation of Mathematical
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[17] J. Wu, Theory and Applications of Parical Functional Differential
Equations, Springer-Verlag, New York, 1996.
[18] J. Wu and X. Zou, Travling wave fronts of reaction-diffusion systems
with delay, J. Dynamics and Differential Equations, 13 (2001), 651-687.
[19] X. Q Zhao and Z. T. Jing, Global asymptotic behavior in some cooperative
systems of functional differential equations, Canadian Applied
Mathematics Quarterly, 4 (1996), 421-444.
[20] X. Q. Zhao and W. Wang, Fisher waves in an epidemic model, Disc.
Conti. Dyn. Sys. Ser. B4 (2004), 1117-1128.
指導教授 許正雄(Cheng-hsiung Hsu) 審核日期 2012-7-12
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