論擴散-競爭型洛特卡-佛爾特拉方程組的3物種行波解研究

Shun-Chieh Wang; 王舜傑

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69446

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DC 欄位	值	語言
dc.contributor.advisor	陳俊全
dc.contributor.author	Shun-Chieh Wang	en
dc.contributor.author	王舜傑	zh_TW
dc.date.accessioned	2021-06-17T03:15:55Z	-
dc.date.available	2018-07-06
dc.date.copyright	2018-07-06
dc.date.issued	2018
dc.date.submitted	2018-07-05
dc.identifier.citation	[1] H. KOKUBU, Homoclinic and heteroclinic bifurcations of vector fields, Japan J. Appl. Math., 5(1988),pp. 455-501 [2] YUKIO KAN-ON, Parameter dependence of propagation speed of travelling waves for competition-diffusion equations, SIAM J. MATH. ANAL. Vol. 26, No. 2, pp. 340-363, March 1995 [3] Berestycki H, Diekmann O, Nagelkerke CJ, Zegeling PA, Can a species keep pace with a shifting climate? , Bull. Math. Biol. 71,399–429 (2009) [4] M. Rodrigo, M. Mimura, Exact solutions of a competition-diffusion system , Hiroshima Math. J., 30 (2000),pp. 257-270 [5] K. J. Palmer, Exponential dichotomies and transversal homoclinic points. J. Differential Equations,55 (1984), 225-256. [6] E. A. Coddington and N. Levinson, Theory of differential equations, McGraw-Hill, New-York, 1955. [7] W. A. Coppel, Dichotomies in Stability Theory, Springer-Verlag, Berlin, 1978.
dc.identifier.uri	http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69446	-
dc.description.abstract	本篇論文是研究 Lotka-Volterra 3 物種競爭的行波解之解的存在性問題，主要是延伸 Kanon 在 1995 年，所證明的雙物種經爭行波解的存在唯一性。我們將證明，在 w 物種與 u,v 物種之間競爭影響力很小時，以及 u-v 物種具有強競爭的情況下，可以利用 Perturbation method 將 2 物種的解擾動一點點，而得到新的帶有 source term 之 2 物種問題的解。但是找到的解勢必要同時滿足三個方程式，所以需要一些 iteration argument 去逼近 3 物種的解。	zh_TW
dc.description.abstract	In this thesis, we study the Lotka-Volterra 3 species competition model. We first introduce the conclusion of existence of 2-species traveling wave solution. Next, the main idea to prove the existence of 3-species traveling wave solution is the perturbation method and the iteration argument. We will prove that when the competition rate between w and both u & v is small enough, other parameters satisfy some suitable condition, then there exist a nontrivial 3-species traveling wave solution.	en
dc.description.provenance	Made available in DSpace on 2021-06-17T03:15:55Z (GMT). No. of bitstreams: 1 ntu-107-R05221005-1.pdf: 747164 bytes, checksum: 8e1505e936193fdd18593e82fc9dbda0 (MD5) Previous issue date: 2018	en
dc.description.tableofcontents	1. Introduction...3 2. Main Problem and Result...7 3. Proofs the main theory...9 3.1 Linearized map...17 3.2 Fundamental solution...18 3.3 Perturbation method...19 3.4 Proof Theorem A...35 3.5 Interior estimate...39 3.6 Nonzero and Positivity...44 4. A special case...47 4.1 Example...53 5. APPENDIX...55 5.1 A1...55 6. Reference...56
dc.language.iso	en
dc.subject	擾動理論	zh_TW
dc.subject	行波解	zh_TW
dc.subject	3物種	zh_TW
dc.subject	擴散-競爭型洛特卡-佛爾特拉方程組	zh_TW
dc.subject	iteration	en
dc.subject	3 species	en
dc.subject	competition	en
dc.subject	reaction diffusion model	en
dc.subject	perturbation	en
dc.subject	Lotka-Volterra	en
dc.subject	exponential dichotomy	en
dc.subject	heteroclinic orbit	en
dc.title	論擴散-競爭型洛特卡-佛爾特拉方程組的3物種行波解研究	zh_TW
dc.title	Traveling Wave Solutions of Lotka-Volterra Diffusion Competition System with 3-species	en
dc.type	Thesis
dc.date.schoolyear	106-2
dc.description.degree	碩士
dc.contributor.oralexamcommittee	王振男,林太家
dc.subject.keyword	擴散-競爭型洛特卡-佛爾特拉方程組,3物種,行波解,擾動理論,	zh_TW
dc.subject.keyword	Lotka-Volterra,3 species,competition,reaction diffusion model,perturbation,iteration,exponential dichotomy,heteroclinic orbit,	en
dc.relation.page	56
dc.identifier.doi	10.6342/NTU201801298
dc.rights.note	有償授權
dc.date.accepted	2018-07-05
dc.contributor.author-college	理學院	zh_TW
dc.contributor.author-dept	數學研究所	zh_TW
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