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姓名 李閎嚴(Hung-Yen Lee)  查詢紙本館藏   畢業系所 數學系
論文名稱 離散型Lotka-Volterra競爭系統之行波解的穩定性
(Stability of traveling wavefronts for a discrete Lotka-Volterra competition system)
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摘要(中) 本論文主要研究三物種競爭合作關係之離散型Lotka-Volterra 模型行波解的穩定性問題。透過能量加權方法以及比較原則,在較大的速度下,我們證明了行波解具有指數穩定的特性。
摘要(英) In this thesis, we study the stability of traveling wave solutions for the three species competition cooperation system, which is the discrete version of the Lotka-Volterra system.
Applying the weighted energy method and the comparison principle, we can derive the result that the traveling wavefronts with large speed are exponentially stable.
關鍵字(中) ★ 穩定性
★ Lotka-Volterra
關鍵字(英) ★ stability
★ Lotka-Volterra
論文目次 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Some known results and background . . . . . . . . . . . . . . . . . . . . . 6
3 Stability for traveling wavefronts . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1 Weighted energy estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Derivative estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Proof of Theorem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
參考文獻 [1] P. Ashwin, M. V. Bartuccelli, T. J. Bridges and S. A. Gourley, Travelling fronts for the
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[2] A. Boumenir and V. Nguyen, Perron theorem in monotone iteration method for
traveling waves in delayed reaction-diffusion equations, J. Differential Equations,
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[3] G.-S. Chen, S.-L. Wu and C.-H. Hsu, Stability of traveling wavefronts for a discrete
diffusive competition system with three species, preprint, 2018.
[4] N. Fei and J. Carr, Existence of travelling waves with their minimal speed for a
diffusing Lotka-Volterra system, Nonlinear Analysis: Real World Applications, 4
(2003), 503-524.
[5] X. Hou and Y. Li, Traveling waves in a three species competition-cooperation system,
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[6] C.-H. Hsu, J.-J. Lin and S.-L. Wu, Existence and stability of traveling wave solutions
for discrete three species competitive-cooperative systems, preprint, 2018.
[7] L. Hung, Traveling wave solutions of competitive-cooperative Lotka-Volterra systems
of three species, Nonlinear Analysis: Real World Applications, 12 (2011), 3691-3700.
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指導教授 許正雄(Cheng-Hsiung Hsu) 審核日期 2019-1-19
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