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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/36949完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
| dc.contributor.author | Li-Sheng Chang | en |
| dc.contributor.author | 張立昇 | zh_TW |
| dc.date.accessioned | 2021-06-13T08:24:21Z | - |
| dc.date.available | 2007-07-19 | |
| dc.date.copyright | 2005-07-19 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-07-16 | |
| dc.identifier.citation | [1] R.A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics 7 (1937), 353-369.
[2] I. Kolmogorov, I. Petrovsky and N. Piscounov, Etude de lequation de la diffusion avec croissance de la quantite de matiere et son application a un probleme biologique, Moscow Univ. Bull. Math. 1 (1937), 1-25. [3] E.E. Holmes, M.A. Lewis, J.E. Banks and R.R. Veit, Partial differential equations in ecology: spatial interactions and population dynamics, Ecology 75 (1994), 17-29. [4] J.A. Sherratt and B.P. Marchant, Models of epidermal wound healing, Proc. R. Soc. Lond. B241 (1990), 29-36. [5] R. Luther, Raumliche Fortpflanzug Chemister Reaktionen. Z. fur Elektrochemie und angew. Physikalische Chemie. 12(32),1906. English translation: (R. Arnold, K. Showalter and J.J. Tyson) Propagaation chemical reaction in space, J. Chem. Educ. (1987). [6] W.S.C. Gurney and R.M. Nisbet(1975), The regulation of inhomogeneous population, J. Theor. Biol. 52, 441-457. [7] J.D. Murray, Mathematical Biology, Springer, Berlin, 1993. [8] P.C. Fife, Mathematical Aspects of Reaction and Di using Systems : Lecture Notes in Biomathematics, Vol. 28, Springer, New York, 1979. [9] D.G. Aronson, Density-dependent interaction systems, in : B. Fiedler, et al. (Eds), Dynamics and Modelling of Reactive Systems, Academic Press, New York, 1980, pp. 161-176. [10] F. S anchez-Gardu~ no, and P.K. Maini, Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equation, J. Math. Biol 33 (1994) 163-192. [11] F. S anchez-Gardu~ no, and P.K. Maini, Travelling wave phenomena in some degenerate reaction-di usion equations, J. Di erential Equations 117 (1995) 281-319 doi:10.1006/jdeq. 1995.1055. [12] R.A. Satnoianu, P.K. Maini, F.S. Gardu~ no, and J.P. Armitage, Travelling waves in a nonlinear degenerate di usion model for bacterial pattern formation, Discrete Continuous Dyn. Systems Ser. B 1 (2001) 339-362. [13] L. Malaguti, and C. Marcelli, A comparison-type approach for travelling fronts, in B. Fiedler, et al., (Eds.), International Conference on Differential Equations, Berlin, 1999, World Scienti c, Singapore, 2000, pp. 1220-1225. [14] L. Malaguti, and C. Marcelli, Travelling wavefronts in reaction-diffusion equations with convection e ects and non-regular terms, Math. Nachr.242 (2002) 148-164. [15] L. Malaguti, and C. Marcelli, Sharp pro les in degenerate and doubly degenerate Fisher-KPP equations, J. Differential Equations 195 (2003) 471-496. [16] T. Ogiwara, and H. Matano, Stability analysis in order preserving systems in the presence of symmetry, Proc. Roy. Soc. Edinburgh Sect. A, 129 (1999), pp. 395-438. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/36949 | - |
| dc.description.abstract | 這篇論文討論反應擴散方程在Fisher-KPP及bistable的情形下擴散係數退化所造成的影響。當非線性項是Fisher-KPP時，我們可得到一連串波速c≧c*的行波解，其中波速c=c*時會產生sharp的行波解；當非線性項是bistable時發現所有行波解均為sharp。最後我們利用Min-max方法去估計出sharp行波解之波速。 | zh_TW |
| dc.description.abstract | This paper investigates the effects of a degenerate diffusion term in reaction-diffusion models with Fisher-KPP and bistable type nonlinearities. In the first case when the nonlinear term g is of Fisher-KPP type, we obtain a continuum of t.w.s. having wave speed c greater than a threshold value c* and the appearance of a sharp-type profile if c = c*. In the other case when g is bistable, we observe that the t.w.s. is of sharp type. Finally, we estimate the speed of front propagation for reaction-diffusion equations. This formulation makes it possible to calculate sharp estimates for the speed explicitly. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T08:24:21Z (GMT). No. of bitstreams: 1 ntu-94-R92221016-1.pdf: 139918 bytes, checksum: b5c2f728b81023473d904877cdca7b8f (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | 1 Introduction 1
2 Continuum of travelling wave solutions of Fisher-KPP type 3 3 First-order singular problem for travelling wave solutions with bistable type 8 4 Characterization of sharp-type wavefronts 14 5 Min-max principles for the wave speed 15 | |
| dc.language.iso | en | |
| dc.subject | 行波解 | zh_TW |
| dc.subject | 退化型 | zh_TW |
| dc.subject | sharp解 | zh_TW |
| dc.subject | 波速估計 | zh_TW |
| dc.subject | 反應擴散方程 | zh_TW |
| dc.subject | sharp solutions | en |
| dc.subject | Speed estimates | en |
| dc.subject | degenerate | en |
| dc.subject | Reaction-diffusion equations | en |
| dc.subject | Travelling wave solutions | en |
| dc.title | 退化型之反應擴散方程 | zh_TW |
| dc.title | Reaction-diffusion Equations of Degenerate-type | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 93-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 林太家,陳建隆 | |
| dc.subject.keyword | 行波解,反應擴散方程,退化型,sharp解,波速估計, | zh_TW |
| dc.subject.keyword | Travelling wave solutions,Reaction-diffusion equations,degenerate,sharp solutions,Speed estimates, | en |
| dc.relation.page | 18 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-07-19 | |
| 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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