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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69446完整後設資料紀錄
| 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.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 |
| 顯示於系所單位： | 數學系 | |
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