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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
| dc.contributor.author | Chueh-Hsin Chang | en |
| dc.contributor.author | 張覺心 | zh_TW |
| dc.date.accessioned | 2021-06-17T00:21:29Z | - |
| dc.date.available | 2014-06-29 | |
| dc.date.copyright | 2012-06-29 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-06-15 | |
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Variazioni e fluttuazioni del numero d’individui in specie animali conciventi (Variations and fluctuations of the number of individuals in animal species living together)Memoria della R. Accademia Nazionale dei Lincei, Ser. VI 2, 31 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/66091 | - |
| dc.description.abstract | 這篇博士論文分為兩個部分，以考慮兩種由生態學而來的偏微分方程的行波解。第一部份我們考慮三個物種的競爭擴散系統。第二部分是考慮關於雙物種的自由邊界問題。
關於三個物種的競爭擴散系統，其行波解可以考慮為 R^6 中某向量場的異宿軌道 (heteroclinic orbit)。方程的參數在適當的假設下，我們利用異宿軌道的分歧理論來證明，三個物種的行波解可由兩個連接到某個相同平衡點(equilibrium)的雙物種行波解分歧出來。此三物種行波解的每一個部分都是正解。其波形為：其中一個物種連接某個正態(positive state)到零，另一物種連接零到某個正態， 第三物種為介於以上兩物種中間，在某個長區間內靠近某正態的脈衝(pulse)。我們對方程的參數，在哪些範圍會有三物種的行波解，找到了某些明確的表現形式，來作為此結果的具體應用。 關於雙物種競爭模型的自由邊界問題，最早是由 Mimura, Yamdada 及 Yotsutani 所提出。基於 Du 和 Lin 的散佈--消滅二分性(spreading-vanishing dichotomy)的結果，我們假設，當時間趨於無窮，自由邊界的散佈速度會趨於某個常數，而由此考慮對應於原自由邊界問題的的行波解問題。我們得出此問題的行波解的存在性與唯一性。 | zh_TW |
| dc.description.abstract | We divide the thesis into two parts to investigate the travelling wave of two types partial differential
equations coming from ecology. In Part 1, we consider the 3-species Lotka-Volterra competition-diffusion systems. In Part 2, we consider a free boundary problem for a two-species competitive model. For the 3-species Lotka-Volterra competition-diffusion system, a travelling wave solution can be considered as a heteroclinic orbit of a vector field in R^6. Under suitable assumptions on the parameters of the equations, we apply a bifurcation theory of heteroclinic orbits to show that a 3-species travelling wave can bifurcate from two 2-species waves which connect to a common equilibrium. The three components of the 3-species wave obtained are positive and have the profiles that one component connects a positive state to zero, one component connects zero to a positive state, and the third component is a pulse between the previous two with a long middle part close to a positive constant. As concrete examples of application of our result, we find several explicit regions of the parameters of the equations where the bifurcations of 3-species travelling waves occur. The free boundary problem for a two-species competitive model in ecology was proposed by Mimura, Yamada and Yotsutani. Motivated by the spreading-vanishing dichotomy obtained by Du and Lin, we suppose the spreading speed of the free boundary tends to a constant as time tends to infinity and consider the corresponding travelling wave problem. We establish the existence and uniqueness of a travelling wave solution for this free boundary problem. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T00:21:29Z (GMT). No. of bitstreams: 1 ntu-101-D94221007-1.pdf: 1476765 bytes, checksum: b1b7f9bd89ace701324d5246ba216a0d (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | Acknowledgements (in Chinese) i
Acknowledgements (in English) iii Abstract (in Chinese) v Abstract (in English) vii 1 Introduction 1 I 3-species Lotka-Volterra competition-diffusion systems 5 2 Introduction, preliminaries and results 7 2.1 Introduction 7 2.2 Preliminaries 18 2.3 Results 22 3 Conditions (H1) to (H4) 27 3.1 Introduction 27 3.2 Conditions (H1) to (H4) 27 3.3 Proof of (H1) 30 3.4 Proof of (H2) 31 ix3.5 Proof of (H3) 39 3.6 Solutions of y0 = − y∂ Y F (h 1 (z), µ 0 ) and exponential dichotomy 49 3.7 Proof of (H4) 54 4 Proof of the results 61 4.1 Introduction 61 4.2 Proof of Theorem 2.3.1: existence of O i − O i+1 connection 62 4.3 Existence of 3 species waves 65 4.3.1 Proof of Theorem 2.3.2 (1), (2), (3): existence of O 1 − O 3 con-nection 65 4.3.2 Proof of Theorem 2.3.2 (4): positivity of 3-species waves 77 5 Existence of bifurcation points 85 5.1 Introduction 85 5.2 Proof of Theorem 2.3.4 86 5.2.1 Proof of Theorem 2.3.4 (1): Bifurcation points with speed equals zero 86 5.2.2 Proof of Theorem 2.3.4 (2): Bifurcation points with speed close to zero 91 5.3 Proof of Theorem 2.3.7: ODE stability 92 5.3.1 Proof 92 5.3.2 Strong competition between the three species u, v and w 93 5.4 Proof of Theorem 2.3.5 and Theorem 2.3.6 94 5.4.1 Theorem 2.3.5: general diffusion rate 95 5.4.2 Theorem 2.3.6: d v = d w = 1 96 6 Discussion and conclusions 99 6.1 Introduction 99 6.2 A remark on (H3) 99 x6.2.1 Introduction 99 6.2.2 λ +u = Λ +1 100 6.2.3 η− u = H−3 102 6.2.4 Other cases 104 6.3 Discussion 104 7 Appendix 107 7.1 Introduction 107 7.2 A stable manifold theorem for non-autonomous linear ordinary differ- ential equations 107 7.3 Asymptotic behaviors of fundamental solutions of L φ (U) = 0, L ψ (U)=0 109 7.3.1 Introduction 109 7.3.2 Fundamental solutions of L±φ(U) = 0, L± ψ(U)=0 110 7.3.3 Partial comparison principle 114 7.3.4 Fundamental solutions of L φ (U) = 0 and L ψ (U) = 0 117 7.4 Proof of estimates modified from Fife and Mimura’s paper 125 7.4.1 Preliminaries 125 7.4.2 Proof of Lemma 5.2.1 130 II Free boundary problem for a two-species competitive model 135 8 Introduction, results and proof 137 8.1 Introduction 137 8.2 Proof of the theorems 143 8.2.1 Proof of Theorem 8.1.1: non-zero latent heat 149 8.2.2 Proof of Theorem 8.1.2: zero and non-zero latent heat 152 8.3 Some remarks about the Stefan condition 153 xiIII List of symbols 155 9 List of symbols 157 | |
| dc.language.iso | en | |
| dc.subject | 散佈速度 | zh_TW |
| dc.subject | 競爭擴散系統 | zh_TW |
| dc.subject | 異宿分歧 | zh_TW |
| dc.subject | 行波解 | zh_TW |
| dc.subject | KPP型態方程 | zh_TW |
| dc.subject | 自由邊界問題 | zh_TW |
| dc.subject | competition-diffusion system | en |
| dc.subject | spreading speed | en |
| dc.subject | free boundary problem | en |
| dc.subject | KPP type equation | en |
| dc.subject | travelling waves | en |
| dc.subject | heteroclinic bifurcation | en |
| dc.title | 競爭擴散系統的行波解 | zh_TW |
| dc.title | Travelling Wave Solutions of Competition-Diffusion Systems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 陳宜良(I-Liang Chern),陳建隆(Jann-Long Chern),郭忠勝(Jong-Shenq Guo),夏俊雄(Chun-Hsiung Hsia),林太家(Tai-Chia Lin) | |
| dc.subject.keyword | 競爭擴散系統,異宿分歧,行波解,KPP型態方程,自由邊界問題,散佈速度, | zh_TW |
| dc.subject.keyword | competition-diffusion system,heteroclinic bifurcation,travelling waves,KPP type equation,free boundary problem,spreading speed, | en |
| dc.relation.page | 182 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2012-06-18 | |
| 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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