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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
| dc.contributor.author | Li-Chang Hung | en |
| dc.contributor.author | 洪立昌 | zh_TW |
| dc.date.accessioned | 2021-06-17T00:48:35Z | - |
| dc.date.available | 2021-06-20 | |
| dc.date.copyright | 2012-01-17 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-12-08 | |
| dc.identifier.citation | [1] M. J. Ablowitz and A. Zeppetella, Explicit solutions of Fisher’s equation for
a special wave speed, Bull. Math. Biol., 41 (1979), pp. 835–840. [2] G. A. Afrouzi, On a nonlinear eigenvalue problem in ODE, J. Math. Anal. Appl., 303 (2005), pp. 342–349. [3] S. Ahmad and A. C. Lazer, An elementary approach to traveling front solutions to a system of N competition-diffusion equations, Nonlinear Anal., 16 (1991), pp. 893– 901. [4] D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in Partial differential equations and related topics (Program, Tulane Univ., New Orleans, La., 1974), Springer, Berlin, 1975, pp. 5–49. Lecture Notes in Math., Vol. 446. [5] C.-C. Chen, L.-C. Hung, M. Mimura, and D. Ueyama, Exact traveling wave solutions of three species competition-diffusion systems, preprint. [6] , Traveling waves with two humps in a competitive lotka-volterra system of three species, preprint. [7] R. Cherniha and V. Davydovych, Conditional symmetries and exact solutions of the diffusive lotka-volterra system, Mathematical and Computer Modelling, 54 (2011), pp. 1238 – 1251. [8] P. de Mottoni, Qualitative analysis for some quasilinear parabolic systems, Institute of Math., Polish Academy Sci., Zam, 190 (1979), pp. 11–79. [9] N. Fei and J. Carr, Existence of travelling waves with their minimal speed for a diffusing Lotka-Volterra system, Nonlinear Anal. Real World Appl., 4 (2003), pp. 503–524. [10] P. Fife and J. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Archive for Rational Mechanics and Analysis, 65 (1977), pp. 335–361. [11] P. C. Fife, Mathematical aspects of reacting and diffusing systems, vol. 28 of Lecture Notes in Biomathematics, Springer-Verlag, Berlin, 1979. [12] R. A. Fisher, The wave of advance of an advantageous gene, Ann. Eugen, 7 (1936), pp. 355–369. [13] X. Hou and A. W. Leung, Traveling wave solutions for a competitive reactiondiffusion system and their asymptotics, Nonlinear Anal. Real World Appl., 9 (2008), pp. 2196–2213. [14] L.-C. Hung, Traveling wave solutions of competitive-cooperative lotka-volterra systems of three species, Nonlinear Analysis: Real World Applications, 12 (2011), pp. 3691 – 3700. [15] Y. Kan-on, Parameter dependence of propagation speed of travelling waves for competition-diffusion equations, SIAM J. Math. Anal., 26 (1995), pp. 340–363. [16] , Existence of standing waves for competition-diffusion equations, Japan J. Indust. Appl. Math., 13 (1996), pp. 117–133. [17] , Fisher wave fronts for the Lotka-Volterra competition model with diffusion, Nonlinear Anal., 28 (1997), pp. 145–164. [18] , Travelling waves for a Lotka-Volterra competition model with diffusion [translation of S‾ugaku 49 (1997), no. 4, 379–392; MR1614330 (2000b:92020)], Sugaku Expositions, 13 (2000), pp. 39–53. Sugaku Expositions. [19] J. I. Kanel, On the wave front solution of a competition-diffusion system in population dynamics, Nonlinear Anal., 65 (2006), pp. 301–320. [20] J. I. Kanel and L. Zhou, Existence of wave front solutions and estimates of wave speed for a competition-diffusion system, Nonlinear Anal., 27 (1996), pp. 579–587. [21] , Existence of wave front solutions and estimates of wave speed for a competitiondiffusion system, Nonlinear Anal., 27 (1996), pp. 579–587. [22] P. Koch Medina and G. Sch atti, Long-time behaviour for reaction-diffusion equations on RN, Nonlinear Anal., 25 (1995), pp. 831–870. [23] A. Kolmogoroff, I. Petrovsky, and N. Piscounoff, Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem.(French) Moscow Univ, Bull. Math, 1 (1937), pp. 1–25. [24] A. W. Leung, Nonlinear Systems of Partial Differential Equations, Applications to Life and Physical Sciences, World Scientific Publishing Co., New Jersey, Singapore, London, 2009. [25] A. W. Leung, X. Hou, and W. Feng, Traveling wave solutions for Lotka- Volterra system re-visited, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), pp. 171– 196. [26] , Traveling wave solutions for Lotka-Volterra system re-visited, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), pp. 171–196. [27] A. W. Leung, X. Hou, and Y. Li, Exclusive traveling waves for competitive reaction-diffusion systems and their stabilities, J. Math. Anal. Appl., 338 (2008), pp. 902–924. [28] S. Merino, A note on the existence of travelling waves for the Fisher-Kolmogorov equation via the method of sub- and supersolutions, in International Conference on Differential Equations (Lisboa, 1995), World Sci. Publ., River Edge, NJ, 1998, pp. 448–452. [29] J. D. Murray, Mathematical biology, vol. 19 of Biomathematics, Springer-Verlag, Berlin, second ed., 1993. [30] M. Rodrigo and M. Mimura, Exact solutions of a competition-diffusion system, Hiroshima Math. J., 30 (2000), pp. 257–270. [31] M. Rodrigo and M. Mimura, Exact solutions of reaction-diffusion systems and nonlinear wave equations, Japan J. Indust. Appl. Math., 18 (2001), pp. 657–696. [32] M. Tang and P. Fife, Propagating fronts for competing species equations with diffusion, Archive for Rational Mechanics and Analysis, 73 (1980), pp. 69–77. [33] A. I. Volpert, V. A. Volpert, and V. A. Volpert, Traveling wave solutions of parabolic systems, vol. 140 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, 1994. Translated from the Russian manuscript by James F. Heyda. [34] J. Wu and X. Zou, Traveling wave fronts of reaction-diffusion systems with delay, J. Dynam. Differential Equations, 13 (2001), pp. 651–687. [35] , Erratum to: “Traveling wave fronts of reaction-diffusion systems with delay” [J. Dynam. Differential Equations 13 (2001), no. 3, 651–687; mr1845097], J. Dynam. Differential Equations, 20 (2008), pp. 531–533. [36] L. Zhou and Y. I. Kanel, A new proof of existence of the wave front solutions for a kind of reaction-diffusion system, in Nonlinear evolutionary partial differential equations (Beijing, 1993), vol. 3 of AMS/IP Stud. Adv. Math., Amer. Math. Soc., Providence, RI, 1997, pp. 469–481. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/66647 | - |
| dc.description.abstract | 本作品討論二物種與三物種擴散型洛特卡-佛爾特拉方程組。對二競爭物種組，雙曲函數法用來構建嚴密行進波解。在藤田型結果的基礎之上，發展共存位移法來找二合作物種組的爆破解(和廖嫻)。對競爭-合作混合型三物種組，我們用上下解法來構築行進波解的存在性。以廣義雙曲函數法，可以證明三競爭物種組有嚴密(和三村昌泰等人)和半嚴密行進波解(和裘愉生)。此外，藉由極大值原理，三競爭物種組的行進波解不存在性也可以建立。最終，我們證明由熱傳方程的解可以構造出三競爭物種擴散型組的解。更進一步工作包含如何研究由擴散項引發的長期共存，這是從熱傳方程的解構築出來之解所發現的有趣新現象。 | zh_TW |
| dc.description.abstract | In the present work, we study diffusive Lotka-Volterra systems of two-species and three-species. For competitive systems of two species, the tanh method is applied to construct exact traveling wave solutions. Based on the Fujita-type results, the method of shifted coexistence is developed to find blow-up solutions of cooperative systems of two species (with Xian Liao). For competitive-cooperative and competitive systems of three species, we employ the method of super- and subsolutions to establish the existence of traveling wave solutions. By using the generalized tanh method, it is shown that exact (with M. Mimura et al.) and semi-exact (with Yu-Sheng Chiou) traveling wave solutions exist for competitive systems of three species. In addition, nonexistence of traveling wave solutions to competitive systems of three species is also established by the maximum principle. Finally, we show solutions to competitive systems of three species can be constructed from the solutions of the heat equation. Further investigations include how to study diffusion-enhanced long-term coexistence, which is an interesting new phenomenon discovered by means of the solutions constructed from the heat equation. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T00:48:35Z (GMT). No. of bitstreams: 1 ntu-100-D93221004-1.pdf: 627292 bytes, checksum: 6378584096330b27b829b98a7c3a2303 (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 1 Introduction 1
I Lotka-Volterra Systems of Two-Species 3 2 Competition Models: Tanh method 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Exact traveling wave solutions . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 (e1, e2)-waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 (e1, e4)-waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.3 (e2, e3)-waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.4 (e2, e4)-waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Cooperation Models: Shifted-Coexistence Method 19 3.1 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 An illustrative example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 II Lotka-Volterra Systems of Three-Species 25 4 Diffusion-enhanced long-term coexistence: approach to constructing solutions for a diffusive Lotka-Volterra system from solutions of the heat equation 27 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.3 Diffusion-enhanced long-term coexistence . . . . . . . . . . . . . . . . . . 36 4.4 Alternative approach to space-time separated solutions: the method of exp-sin functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.5 Illustrative examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5 Nonmonotone Traveling Wave Solutions for Diffusive Lotka-Volterra Systems of Three Competing Species 51 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.3 The Main Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6 Traveling Wave Solutions of Competitive-Cooperative Lotka-Volterra Systems of Three Species 59 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.3 Existence of Traveling Fronts . . . . . . . . . . . . . . . . . . . . . . . . 65 6.4 Exact Traveling Wave Solutions . . . . . . . . . . . . . . . . . . . . . . . 70 6.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 7 Nonexistence of Traveling Wave Solutions 73 7.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 7.2 Main result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 8 Semi-Exact Traveling Wave Solutions 77 8.1 Semi-exact two-humps solutions . . . . . . . . . . . . . . . . . . . . . . . 77 8.2 Semi-exact nonmonotone traveling wave solutions . . . . . . . . . . . . . 82 8.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 8.2.2 Type-I Solutions: (i, m, n) = (2, 4, 1) . . . . . . . . . . . . . . . . 82 8.2.3 Type-II Solutions: (i, m, n) = (3, 1, 2) . . . . . . . . . . . . . . . . 84 8.2.4 Type-III Solutions: (i, m, n) = (3, 2, 2) . . . . . . . . . . . . . . . 85 8.2.5 Type-IV Solutions: (i, m, n) = (3, 4, 1) . . . . . . . . . . . . . . . 86 8.2.6 Type-V Solutions: (i, m, n) = (4, 1, 1) . . . . . . . . . . . . . . . . 87 8.2.7 Type-VI Solutions: (i, m, n) = (2, 4, 1) . . . . . . . . . . . . . . . 88 8.2.8 Type-VII Solutions: (i, m, n) = (4, 3, 1) . . . . . . . . . . . . . . . 89 | |
| dc.language.iso | en | |
| dc.subject | 行進波解 | zh_TW |
| dc.subject | 嚴密解 | zh_TW |
| dc.subject | 洛特卡-佛爾特拉 | zh_TW |
| dc.subject | Lotka-Volterra | en |
| dc.subject | Traveling wave solutions | en |
| dc.subject | Exact solutions | en |
| dc.title | 論洛特卡-佛爾特拉方程組之解 | zh_TW |
| dc.title | On Solutions of Diffusive Lotka-Volterra Systems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 陳宜良(I-Liang Chern),陳建隆(Jann-Long Chern),郭忠勝(Jong-Sheng Guo),夏俊雄(Chun-Hsiung Hsia),林太家(Tai-Chia Lin) | |
| dc.subject.keyword | 行進波解,嚴密解,洛特卡-佛爾特拉, | zh_TW |
| dc.subject.keyword | Traveling wave solutions,Exact solutions,Lotka-Volterra, | en |
| dc.relation.page | 93 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2011-12-09 | |
| 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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