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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
| dc.contributor.author | Chih-Chiang Huang | en |
| dc.contributor.author | 黃志強 | zh_TW |
| dc.date.accessioned | 2021-05-17T09:19:16Z | - |
| dc.date.available | 2014-07-19 | |
| dc.date.available | 2021-05-17T09:19:16Z | - |
| dc.date.copyright | 2012-07-19 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-02 | |
| dc.identifier.citation | [1] Benci, V. and Rabinowitz, P. H., Critical point theorems for indefinite functionals,
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A. and Mitidieri, E., Standing wave solutions for a system derived from the FitzHugh-Nagumo equations for nerve conduction, SIAM J. Math. Anal. 17 (1986), no. 1, 74-83. [21] Kokubu, H., Nishiura, Y. and Oka, H., Heteroclinic and homoclinic bifurcations in bistable reaction diffusion systems, J. Differential Equations 86 (1990), no. 2, 260-341. [22] Klaasen, G. A. and Troy, W. C., Stationary wave solutions of a system of reaction-diffusion equations derived from the FitzHugh-Nagumo equations, SIAM J. Appl. Math. 44 (1984), no. 1, 96-110. [23] Kurokawa, Y. and Taniguchi, M., Multi-dimensional pyramidal travelling fronts in the Allen-Cahn equations, Proc. Roy. Soc. Edinburgh Sect. A 141 (2011), no. 5, 1031-1054. [24] Lucia, M., Muratov, C. B. and Novaga, M., Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium, Comm. Pure Appl. Math. 57 (2004), no. 5, 616-636. [25] Lucia, M., Muratov, C. 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M. and Goldstein, R. E., Nonlocal contour dynamics model for chemical front motion, Phys. Rev. Lett. 72 (1994), 1120-1123. [38] Reinecke, C. and Sweers, G., A positive solution on RN to a system of elliptic equations of FitzHugh-Nagumo type, J. Differential Equations 153 (1999), no. 2, 292- 312. [39] Reinecke, C. and Sweers, G., Existence and uniqueness of solutions on bounded domains to a FitzHugh-Nagumo type elliptic system, Paci_c J. Math. 197 (2001), no. 1, 183-211. [40] Rinzel, J. and Terman, D., Propagation phenomena in a bistable reaction diffusion system, SIAM J. Appl. Math. 42 (1982), no. 5, 1111-1137. [41] Taniguchi, M., Traveling fronts of pyramidal shapes in the Allen-Cahn equations, SIAM J. Math. Anal. 39 (2007), no. 1, 319-344. [42] Vitolo, A., On the Phragmen-Lindelof principle for second-order elliptic equations, J. Math. Anal. Appl. 300(2004), no. 1, 244-259. [43] Volpert, A. and Volpert, V., Existence of multidimensional travelling waves and systems of waves, Comm. Partial Differential Equations 26(2001), no. 3-4, 421-459. [44] Wei, J. and Winter, M., Standing waves in the FitzHugh-Nagumo system and a problem in combinatorial geometry, Math. Z. 254 (2006), no. 2, 359-383. [45] Yanagida, E., Mini-maximizers for reaction-diffusion systems with skew-gradient structure, J. Differential Equations, 179(2002), no. 1, 311-335. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/6841 | - |
| dc.description.abstract | 本篇論文主要研究在N維空間中擴散的費滋漢那古默系統行波解之存在性。這個系統有反梯度結構亦有非局部的梯度結構。此外，藉由適當的變換它在某些參數範圍之下亦有單調系統結構。
對於有界區域，變分法用來建構此系統有邊值條件平衡態的存在性。無界柱狀區域並且當方程的擴散系數相同時，我們藉由上述的三種結構來研究行波解。使用非局部的能量來證明行波解的存在性並用能量觀點刻畫波速；另一方面，使用反梯度結構，我們給出波與波速的最大最小能量公式刻畫方法。關於全空間區域，應用上解下解法來建立在N維空間中單邊穩定形式之行波解。除此之外，藉著反射方法也建立了在1維空間中無窮多個周期駐波。 | zh_TW |
| dc.description.abstract | In this thesis, we study the existences of travelling waves of the diffusive FitzHugh-Nagumo system (DFHN) in R^N. This system has a skew-gradient structure as defined by Yanagida as well as a non-local gradient structure. In addition, by a suitable transformation, it also has a monotone-system structure on some parameter ranges. For bounded domains, the variational approach is applied to construct steady states of (DFHN) with Dirichlet or/and Neumann condition. For unbounded cylindrical domains, we study the travelling wave solutions via all of the three structures mentioned above when the diffusion coefficients in the equations are equal. By using the nonlocal variational energy, we establish the existence of a travelling front solution for (DFHN). Our existence result also obtains a variational characterization for the wave speed. On the other hand, using the skew-gradient structure, we give a mini-max formulation of the travelling wave and its speed. For whole domains, we employ the method of super- and subsolutions to establish the existence of monostable-type traveling wave solutions in R^N. Moreover, we construct infinitely many standing periodic solutions in R^1 based on the reflection method. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-17T09:19:16Z (GMT). No. of bitstreams: 1 ntu-101-D95221001-1.pdf: 655736 bytes, checksum: e598e50538a41c248f2e81d3796860e1 (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 1 Introduction.............................................1
2 Literature review........................................3 2.1 Steady states on bounded domains.......................4 2.1.1 Bistable cases.......................................4 2.1.2 Monostable cases.....................................5 2.2 Travelling waves in R^1................................6 2.2.1 Bistable cases.......................................6 2.2.2 Monostable cases.....................................7 2.3 Standing waves in R^N..................................7 3 Steady states on bounded domains and periodic solutions in R^N.....................................................9 3.1Introduction............................................9 3.2 Proof of the main theorem.............................10 4 Monostable-type solutions in R^N........................13 4.1 Introduction..........................................13 4.2 Proof of the main theorem.............................15 5 Travelling waves in a cylinder for bistable cases.......21 5.1 Introduction..........................................21 5.2 Preliminaries.........................................26 5.2.1 Basic properties of the weighted Sobolev space......26 5.2.2 Non-local operator..................................27 5.3 Variational approach..................................29 5.3.1 Boundedness and lower semicontinuity of the energy............................................29 5.3.2 Continuity of minimal energy......................32 5.3.3 Estimates for the travelling speed................33 5.4 Existences and properties of minimizers with negative energy................................................34 5.5 Existence of travelling solution......................37 5.6 Skew-gradient structure...............................40 5.7 Neumann problem.......................................42 5.8 Appendix..............................................43 Bibliography..............................................45 | |
| dc.language.iso | en | |
| dc.title | 在N 維空間中的費滋漢那古默系統之行波解 | zh_TW |
| dc.title | Travelling wave solutions of the diffusive FitzHugh-Nagumo
system in R^N | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 林太家(Tai-Chia Lin),陳宜良(I-Liang Chern),夏俊雄(Chun-Hsiung Hsia),郭忠勝(Jong-Shenq Guo),石志文(Chih-Wen Shih) | |
| dc.subject.keyword | 費滋漢那古默系統,行波解,反梯度系統,變分法,上解下解法, | zh_TW |
| dc.subject.keyword | FitzHugh-Nagumo system,travelling waves,skew-gradient structure,variational method,the method of super- and subsolutions, | en |
| dc.relation.page | 48 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2012-07-03 | |
| 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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