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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
| dc.contributor.author | Chu-Chien Lu | en |
| dc.contributor.author | 呂居謙 | zh_TW |
| dc.date.accessioned | 2021-06-16T06:56:57Z | - |
| dc.date.available | 2017-07-29 | |
| dc.date.copyright | 2014-07-29 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-07-18 | |
| dc.identifier.citation | [1] S. Allen and J.W. Cahn, A microscopic theory for antiphase boundary motion
and its application to antiphase domain coarsening, Acta. Metall. 27 (1979), pp. 1084-1095. [2] E. De Giorgi, Convergnece problems for functionals and operators, In: Proc. Int. Meeting on Recent Methods in Nonlinear Analysis, Rome, 1978, Pitagora, 1979, pp. 131-188. [3] N. Ghoussoub, C. Gui, On a conjecture of De Giorgi and some related problems, Math. Ann. 311 (1998), no. 3, 481-491. [4] L. Ambrosio, X. Cabr e, Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi, J. Amer. Math. Soc. 13 (2000), 725-739. [5] O. Savin, Phase Transitions, Minimal Surfaces and A Conjecture of De Giorgi, Current Developments in Mathematics Volume 2009 (2010), 1-204 [6] M. del Pino, M. Kowalczyk, and JunchengWei A counterexample to a conjecture by De Giorgi in large dimensions C. R. Acad. Sci. Paris, Ser. I 346 (2008) 1261-1266 [7] X.F. Chen, J.S. Guo, F. Hamel, H. Ninomiya, and J.M. Roquejo re, travelling waves with paraboloid Di erential Equations, 206:399 437, 2004. 20 [8] H. Ninomiya and M. Taniguchi, Existence and global stability of travelling curved fronts in the Allen-Cahn equations, J. Di erential Equations 213 (2005), no. 1, 204{233. [9] H. Ninomiya and M. Taniguchi. Global stability of travelling curved fronts in the Allen{Cahn equations. Discrete Contin. Dynam. Syst.15(2006), 819{832 [10] Y.Kurokawa, M. Taniguchi, Multi-dimensional pyramidal travelling fronts in the Allen-Cahn equations, Proceedings of the Royal Society of Edinburgh, 141A, 1031-1054, 2011 [11] W.M Ni, and M. Taniguchi, travelling fronts of pyramidal shaped in competition- di usion systems, Networks and Heterogeneous Media, Vol. 8, Num. 1(2013), 379-395. [12] C.D. Levermore, J.X. Xin, Multidimensional sstability of travelling waves in a bistable reaction-di usion equation II, Comm. in Partial Di erential Equation 17 (1992) 1901-1924. [13] H. Matano, M. Nara, M. Taniguchi, Stability of planar waves in the Allen-Cahn equations, Comm. in Partial Di erential Equations Vol.34 (2009) 976-1002. [14] W.J Cheng, W.T Li, and Z.C. Wang, Multidimensional stability of V -shaped travelling fronts in the allen Cahn euqation. Sci China Math, 2013, 56: 1969- 1982, doi: 10.1007/s11425-013-4699-5. [15] M. Taniguchi, The uniqueness and asymptotic stability of pyramidal travelling fronts in the Allen-Cahn equations, Journal of Di erential Equations Vol. 237, No 1. (2007), 61-76 [16] D. Sattinger, On the stability of travelling waves, Adv. in Math., 22(1976), 312-355. 21 [17] P.C. FIFE AND J.B. Mcleod, The approach of solutions of non-linear di usion equations to traveling front solutions, Arch. Rational Mech. Anal. 65 (1977), pp. 335-361. [18] Y.H. Du, Z.M. Gou, The stefan problem for the Fisher-KPP equation, Journal of Di erential Equations 253(2012), p.996-1035 [19] Y.H.Du, Z.M. Gou, Spreading-vanishing dichotomy in a di usive logistic model with a free boundary, II, J. Di erential Equations, 250(2011),pp.4336{4366 [20] D.H. Sattinger Monotone Methods in Nonlinear Elliptic and Parabolic Bound- ary Value Problems, Indiana University Mathematics Journal, Vol.21, No. 11, p.979-1000, 1972. [21] M.H. Protter, H.F. Weinberger, Maximum Principles in Di erential Equations, Prentice-Hall, 1967. [22] Y.H. Du, B.D Lou, Spreading and vanishing in nonlinear di usion problems with free boundaries, J. Eur. Math. Soc., to appear. (arXiv 1301.5373) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/57667 | - |
| dc.description.abstract | 本文探討由建造上下解以及使用單調疊代法來建構的高維度的Allen-Cahn方程式
ut = DΔ u + f(u)的非平面行波解，並透過此種方法來討論其自由邊界問題的上下解以及金字塔型的的存在之可能性. | zh_TW |
| dc.description.abstract | In this thesis, we discuss the non-planar travelling wave solution for the Allen-Cahn reaction-diffusion equation in high dimension ut = D Δu + f(u) by constructing super-sub solutions and use the monotonic iteration method. Also,
we use this method to discuss the super-solution and sub-solution for free boundary problem and also the possibility of the existence of a pyramidal-shaped solution. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T06:56:57Z (GMT). No. of bitstreams: 1 ntu-103-R01221003-1.pdf: 387262 bytes, checksum: 6c4035ec8f0f8d4c2b848305e62881ed (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 致謝 i
中文摘要 ii 英文摘要 iii 1 Introduction 1 1.1 Reaction-Diusion equation: the travelling wave solution for bistable case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The free boundary problem, Stefan Condition . . . . . . . . . . . . . 2 2 Pyramidal Shaped Travelling Fronts 3 2.1 Monotone Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Pyramid and the weak sub-solution . . . . . . . . . . . . . . . . . . . 6 2.3 Super-solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Proof of Main Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Discussion on Free Boundary Problem 15 3.1 Weak Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Spreading-Vanishing Dichotomy . . . . . . . . . . . . . . . . . . . . . 16 3.3 Survey on Pyramidal Shaped Solution . . . . . . . . . . . . . . . . . 17 參考書目 20 | |
| dc.language.iso | zh-TW | |
| dc.subject | 反應擴散方程 | zh_TW |
| dc.subject | 自由邊界問題 | zh_TW |
| dc.subject | 金字塔型 | zh_TW |
| dc.subject | 行波? | zh_TW |
| dc.subject | free boundary problem | en |
| dc.subject | reaction-diffusion equation | en |
| dc.subject | travelling wave solutions | en |
| dc.subject | pyramidal-shaped | en |
| dc.title | 高維度的Allen-Cahn方程之非平面行波解及相關問題 | zh_TW |
| dc.title | High Dimensional Non-planar travelling Wave Solution for
Allen-Cahn Equation and Related Topics | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王藹農(Ai-Nung Wang),夏俊雄(Chun-Hsiung Hsia) | |
| dc.subject.keyword | 反應擴散方程,行波?,金字塔型,自由邊界問題, | zh_TW |
| dc.subject.keyword | reaction-diffusion equation,travelling wave solutions,pyramidal-shaped,free boundary problem, | en |
| dc.relation.page | 22 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-07-18 | |
| 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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