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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 陳俊全 | zh_TW |
dc.contributor.advisor | Chiun-Chuan Chen | en |
dc.contributor.author | 楊哲瑋 | zh_TW |
dc.contributor.author | Che-Wei Yang | en |
dc.date.accessioned | 2023-03-19T21:22:55Z | - |
dc.date.available | 2023-12-27 | - |
dc.date.copyright | 2022-07-27 | - |
dc.date.issued | 2022 | - |
dc.date.submitted | 2002-01-01 | - |
dc.identifier.citation | [1] Shair Ahmad and AC Lazer. An elementary approach to traveling front solutions to a system of n competition-diffusion equations. Nonlinear Analysis: Theory, Methods & Applications, 16(10):893–901, 1991.
[2] Donald G Aronson and Hans F Weinberger. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. In Partial differential equations and related topics, pages 5–49. Springer, 1975. [3] Donald G Aronson and Hans F Weinberger. Multidimensional nonlinear diffusion arising in population genetics. Advances in Mathematics, 30(1):33–76, 1978. [4] Chueh-Hsin Chang, Chiun-Chuan Chen, Li-Chang Hung, Masayasu Mimura, and Toshiyuki Ogawa. Existence and stability of non-monotone travelling wave solutions for the diffusive lotka–volterra system of three competing species. Nonlinearity, 33(10):5080, 2020. [5] Chiun-Chuan Chen and Li-Chang Hung. A maximum principle for diffusive lotka–volterra systems of two competing species. Journal of Differential Equations, 261(8):4573–4592, 2016. [6] Chiun-Chuan Chen, Li-Chang Hung, Masayasu Mimura, and Daishin Ueyama. Exact travelling wave solutions of three-species competition–diffusion systems. Discrete & Continuous Dynamical Systems-B, 17(8):2653, 2012. [7] Yan-Yu Chen, Jong-Shenq Guo, and Chih-Hong Yao. Traveling wave solutions for a continuous and discrete diffusive predator–prey model. Journal of Mathematical Analysis and Applications, 445(1):212–239, 2017. [8] Yu-Shuo Chen and Jong-Shenq Guo. Traveling wave solutions for a three-species predator–prey model with two aborigine preys. Japan Journal of Industrial and Applied Mathematics, 38(2):455– 471, 2021. [9] Cheng-Hsiung Hsu Chueh-Hsin Chang and Tzi-Sheng Yang. Computing evans functions for traveling waves of reaction-diffusion systems via fundamental series solutions. preprint. [10] Earl A Coddington and Norman Levinson. Theory of ordinary differential equations. Tata McGraw-Hill Education, 1955. [11] Yanke Du and Rui Xu. Traveling wave solutions in a three-species food-chain model with diffusion and delays. International Journal of Biomathematics, 5(01):1250002, 2012. [12] Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, and Chin-Chin Wu. Traveling wave solutions for a predator–prey system with two predators and one prey. Nonlinear Analysis: Real World Applications, 54:103111, 2020. [13] Li-Chang Hung. Exact traveling wave solutions for diffusive lotka–volterra systems of two competing species. Japan journal of industrial and applied mathematics, 29(2):237–251, 2012. [14] Yukio Kan-On. Parameter dependence of propagation speed of travelling waves for competition-diffusion equations. SIAM journal on mathematical analysis, 26(2):340–363, 1995. [15] Yukio Kan-On and Qing Fang. Stability of monotone travelling waves for competition-diffusion equations. Japan Journal of Industrial and Applied Mathematics, 13(2):343–349, 1996. [16] Yukio Kan-on and Eiji Yanagida. Existence of nonconstant stable equilibria in competition- diffusion equations. Hiroshima mathematical journal, 23(1):193–221, 1993. [17] Guo Lin, Wan-Tong Li, and Mingju Ma. Traveling wave solutions in delayed reaction diffusion systems with applications to multi-species models. Discrete & Continuous Dynamical Systems-B, 13(2):393, 2010. [18] Shiwang Ma. Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem. Journal of Differential Equations, 171(2):294–314, 2001. [19] Marianito Rodrigo and Masayasu Mimura. Exact solutions of a competition-diffusion system. Hiroshima Mathematical Journal, 30(2):257–270, 2000. [20] Marianito Rodrigo and Masayasu Mimura. Exact solutions of reaction-diffusion systems and nonlinear wave equations. Japan journal of industrial and applied mathematics, 18(3):657–696, 2001. [21] Min Ming Tang and Paul C Fife. Propagating fronts for competing species equations with diffusion. Archive for Rational Mechanics and Analysis, 73(1):69–77, 1980. [22] Jianhong Wu and Xingfu Zou. Traveling wave fronts of reaction-diffusion systems with delay. Journal of Dynamics and Differential Equations, 13(3):651–687, 2001. [23] Zhi-Xian Yu and Rong Yuan. Traveling waves for a lotka–volterra competition system with diffusion. Mathematical and Computer Modelling, 53(5-6):1035–1043, 2011. [24] Tianran Zhang and Yu Jin. Traveling waves for a reaction–diffusion–advection predator–prey model. Nonlinear Analysis: Real World Applications, 36:203–232, 2017. | - |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/83905 | - |
dc.description.abstract | 本篇論文主要研究兩物種的羅特卡-弗爾特拉擴散競爭方程組。我們透過研究行波解來了解此系統。我們成功地證明了非單調解的存在性,其中此解連接了兩個平衡態(0,0)和(0,1)。在過去的文獻中,鮮少有這方面相關的研究。然而,此類型的非單調解在生態學中扮演著重要的角色,可以啟發我們發現一些特別現象。我們主要的研究方法是用不動點定理配合適當的上下解去證明解的存在性。我們也運用了縮小區間的手法證明解的右半部逼近行為。此外,藉由證明速度小於某個特定值時不存在解,我們也刻畫了此系統行波的最小速度。 | zh_TW |
dc.description.abstract | We study the two-species Lotka–Volterra competitive system with diffusion. To understand the dynamics of the system, it is fundamental to investigate the traveling wave solutions. We successfully show the existence of non-monotone pulse-front travelling waves connecting the two equilibria (0,0) and (0,1). In the literature, fewer results are known for the existence of such waves. These waves play an important role in ecology and may motivate us to explore other interesting phenomena in the Lotka– Volterra system. Our approach to prove the existence of traveling waves is based on a method by applying Schauder’s fixed point theorem with the help of suitable upper-lower solutions. One of our main breakthroughs is the construction of such appropriate upper-lower solutions for the competition system. We also apply the idea of shrinking rectangles to the derivation of the asymptotic behavior of the right-hand tail. Moreover, by proving the non-existence of traveling wave solutions with speed less than a critical value, we characterize the minimal wave speed of traveling waves for this model. | en |
dc.description.provenance | Made available in DSpace on 2023-03-19T21:22:55Z (GMT). No. of bitstreams: 1 U0001-1406202217251700.pdf: 2061999 bytes, checksum: be0a71c8c0e8553a3d935c1eb049037a (MD5) Previous issue date: 2022 | en |
dc.description.tableofcontents | 口試委員會審定書...................................... i
中文摘要............................................. ii Abstract............................................ iii 目錄................................................. iv 1. Introduction...................................... 1 2. General Theory.................................... 4 3. Upper-Lower-Solutions............................. 5 3.1 The case s < s∗.................................. 6 3.2 The case s = s∗.................................. 9 4. Asymptotic Behavior............................... 14 5. Minimal Speed..................................... 16 References........................................... 17 | - |
dc.language.iso | zh_TW | - |
dc.title | 兩物種的羅特卡-弗爾特拉擴散競爭方程組之非單調行波解 | zh_TW |
dc.title | Non-monotone travelling wave solutions for the two-species Lotka–Volterra competitive system with diffusion | en |
dc.type | Thesis | - |
dc.date.schoolyear | 110-2 | - |
dc.description.degree | 碩士 | - |
dc.contributor.oralexamcommittee | 夏俊雄;陳逸昆 | zh_TW |
dc.contributor.oralexamcommittee | Chun-Hiung Hisa;I-Kun Chen | en |
dc.subject.keyword | 行波解,上下解,不動點,非單調解,羅特卡-弗爾特拉, | zh_TW |
dc.subject.keyword | travelling wave solutions,upper-lower-solutions,Schauder’s fixed point theorem,non-monotone solutions,Lotka-Volterra, | en |
dc.relation.page | 19 | - |
dc.identifier.doi | 10.6342/NTU202200949 | - |
dc.rights.note | 未授權 | - |
dc.date.accepted | 2022-07-13 | - |
dc.contributor.author-college | 理學院 | - |
dc.contributor.author-dept | 數學系 | - |
顯示於系所單位: | 數學系 |
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