博碩士論文 952201006 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:12 、訪客IP:34.204.191.31
姓名 陳冠朋(Kuan-peng Chen)  查詢紙本館藏   畢業系所 數學系
論文名稱 某類網格型微分方程行波解的存在性,唯一性及穩定性
(Existence, Uniqueness and Asymptotic Stability of Traveling Wave Solutions for Some Lattice Differential Equations)
相關論文
★ 遲滯型細胞神經網路之行進波★ 遲滯型細胞神經網絡行進波之結構
★ 網格型微分方程的行進波的數值解★ 某類週期性網格型微分方程行波解之研究
★ 網格型動態系統行波解之研究★ 矩陣值勢能上的sofic測度
★ 在Sofic Shift上的多重碎型分析★ 某類傳染病模型微分方程行波解之研究
★ 某類三維癌症模型之整體穩定性分析★ 三種競爭合作系統之行波解的存在性
★ 離散型Lotka-Volterra競爭系統之行波解的穩定性
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 在這篇論文,我們考慮以下的網格型微分方程$$u’’_n(t)=-g(u_n(t))+lambda f(u_n(t))+sumlimits_{Ngeq|i|geq0}d_iu_{n-i}(t)$$在$(0,infty )$而且$ninBbb Z$,$f$,$gin C^1$,$g$是非遞減函數以及$f$是非線性monostable型。根據[7]和[9]的方法,存在critical speed $c_0$,且使得所有$c>c_0>0$,我們證明存在唯一的行波解。此外,我們也研究介於$0$和$1$之間行波解的漸近穩定性。
摘要(英) In this thesis, we consider the following lattice differential equation $$u’’_n(t)=-g(u_n(t))+lambda f(u_n(t))+sumlimits_{Ngeq|i|geq0}d_iu_{n-i}(t)$$ on $(0,infty )$ with $ ninBbb Z$, where $f,gin C^1$,$g$ is non-decreasing and $f$ is a monostable-type nonlinearity. Following the ideas of [7] and [9], we also show the existence of a critical speed $c_0>0$ such that for all $c>c_0>0$, there exists a unique traveling wave solution of the equations. Furthermore, we also study the asymptotic stability of traveling wave solutions which are bounded between $0$ and $1$.
關鍵字(中) ★ 存在性
★ 唯一性
★ 漸近穩定性
★ 行波解
★ monostable
★ 下解
★ 上解
關鍵字(英) ★ asymptotic stability
★ uniqueness
★ existence
★ monostable
★ supersolution
★ subsolution
★ traveling wave solutions
論文目次 中文摘要...............................................i
英文摘要..............................................ii
Contents.............................................iii
Abstract...............................................1
1 Introduction........................................2
2 Existence of traveling waves........................3
2.1 Construction of subsolutions......................6
2.2 Construction of supersolutions....................9
3 Uniqueness of traveling wave solutions.............12
4 The initial value problem..........................14
5 Asymptotic stability of traveling wave solutions...22
References............................................27
參考文獻 [1] D. G. Aronson, Density dependent interaction diffusion systems, in ”Pro¬ceedings of the Advance Seminar on Dynamics and Modelling of Reactive Systems,” Academic Press, New York, 1980.
[2] D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion and nerve propagation, in ”Partial Differential Equations and Related Topics,” Lecture Notes in Mathematics, Vol. 446, Springer-Verlag, New York, 1975.
[3] C. Atkinson and G. E. H. Reuter, Deterministic epidemic waves, Math. Proc. Cambridge Philos. Soc.80 (1976), 315-330.
[4] P. W. Bates and A. Chmaj, On a discrete convolution model for phase transitions, Arch. Rational Mech. Anal. 150 (1999), 281-305.
[5] M. Bramson, Convergence of solutions of the Kolmogorov equation to traveling waves, Memoirs Amer. Math. Soc. 44 (1983).
[6] K. J. Brown and J. Carr, Deterministic epidemic waves of critical velocity, Math. Proc. Cambridge Philos. Soc. 81 (1977), 431-433.
[7] J. Carr, and A. Chmaj, Uniqueness of traveling waves for nonlocal monostable equations, Amer. Math. Soc. 132, (2004), 2433-2439.
[8] X. Chen, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations 2 (1997), 125-160.
[9] X. Chen, and J.-S. Guo, Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations, J. Differential Equations 184, (2002), 549-569.
[10] Xinfu Chen and J.-S. Guo, Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics, Mathematische Annalen 326 (2003), 123-146.
[11] S.-N. Chow, J. Mallet-Paret, and W. Shen, Traveling waves in lattice dynamical systems, J. Diff. Eqns., 149 (1998), pp. 248-291.
[12] A. De Pablo and J. L. Vazquez, Travelling waves and finite propagation in a reaction-diffusion equation, J. Differential Equations 93 (1991), 19-61.
[13] O. Diekmann and H. G. Kaper, On the bounded solutions of a nonlinear convolution equation, Nonlinear Anal. 2 (1978), 721-737.
[14] William Ellison and Fern Ellison, Prime Numbers, A Wiley-Interscience Publication, John Wiley and Sons, New York; Hermann, Paris, 1985.
[15] T. Erneux and G. Nicolis, Propagation waves in discrete bistable reaction-diffusion systems, Physica D, 67 (1993), pp. 237-244.
[16] P. C. Fife, Mathematical aspects of reacting and diffusing systems, Lecture Notes in Biomathematics 28, Springer-Verlag, 1979.
[17] P. C. Fife and J. B. McLeod, the approach of solutions of nonlinear equations to travelling front solutions, Arch. Rational Mech. Anal. 65 (1977), 335-361.
[18] R. A. Fisher, The advance of advantageous genes, Ann. Eugenics 7 (1937), 355-369.
[19] S.-C. Fu, J.-S. Guo, and S.-Y. Shieh, Traveling wave solutions for some discrete quasilinear parabolic equations, Nonlinear Anal. 48 (2002), 1137-1149.
[20] D. Hankerson and B. Zinner, Wavefronts for a cooperative tridiagonal system of differential equations, J. Dyn. Differential Equations 5 (1993), 359-373.
[21] Y. Hosono, Travelling wave solutions for some density dependent diffusion equations, Japan J. Appl. Math. 3 (1986), 163-196.
[22] C.-H. Hsu and S.-S. Lin, Existence and multiplicity of traveling waves in a lattice dynamical system, J. Diff. Eqns., 164 (2000), pp. 431-450.
[23] C.-H. Hsu, S.-S. Lin and W. Shen, Traveling waves in cellular neural networks, Internat. J. Bifur. and Chaos, 9 (1999), pp. 1307-1319.
[24] C.-H. Hsu and S.-Y. Yang, Structure of traveling waves in delayed cellular neural networks, preprint, 2002.
[25] H. Hudson and B. Zinner, Existence of traveling waves for a generalized discrete Fisher’s equations, Comm. Appl. Nonlinear Anal., 1 (1994), pp. 23-46.
[26] J. P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math., 47 (1987), pp. 556-572.
[27] A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Etude de l’equation de la diffusion avec croissance de la quantite de matiere et son application a un probleme biologique, Bull. Univ. Moskov. Ser. Internat., Sect. A1 (1937), 1-25. A translation in Dynamics of Curved Fronts (Perspectives in Physics Series), by Pierre Pelce (Editor) and A. Libchaber, Academic Press, Boston, 1988.
[28] J. Mallet-Paret, The global structure of traveling waves in spatial discrete dynamical systems, J. Dyn. Diff. Eqns., 11 (1999), pp. 49-127.
[29] J. Mallet-Paret, The Fredholm alternative for functional differential equations of mixed type, J. Dyn. Differential Equations 11 (1999), 1-47.
[30] H. K. McKean, Nagumo’s equation, Adv. Math. 4 (1970), 209-223.
[31] K. Schumacher, Traveling-front solutions for integro-differential equations. I, J. Reine Angew. Math. 316 (1980), 54-70.
[32] B. Shorrocks and I. R. Swingland, ”Living in a Patch Environment,” Oxford University Press, New York, 1990.
[33] P. Weng and J. Wu, Deformation of traveling waves in delayed cellular neural networks, preprint, 2001.
[34] H. F. Weinberger, Asymptotic behavior of a model in population genetics, Nonlinear partial differential equations and applications (Proc. Special Sem., Indiana Univ., Bloomington, Ind., 1976-1977), 47-96. Lecture Notes in Math., Vol. 648, Springer, Berlin, 1978.
[35] H. F. Weinberger, Long-time behavior of a class of biological models, SIAM J. Math. Anal. 13 (1982), 353-396.
[36] D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, NJ, 1941.
[37] J. Wu and X. Zou, Asymptotical and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, J. Diff. Eqns., 135 (1997), pp. 315-357.
[38] J. Wu and X. Zou, Asymptotic and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, J. Differential Equations 135 (1997), 315-357.
[39] J. Wu and X. Zou, Traveling wave fronts of reaction-diffusion systems with delay, J. Dynam. Differential Equations 13 (2001), 651-687.
[40] B. Zinner, Stability of travelling wavefronts for the discrete Nagumo equation, SIAM J.Math. Anal. 22 (1991), 1016-1020.
[41] B. Zinner, Existence of traveling wavefront solutions for discrete Nagumo equation, J. Diff. Eqns., 96 (1992), pp. 1-27.
[42] B. Zinner, G. Harris and W. Hudson, Traveling wavefronts for the discrete Fisher’s equation, J. Differential Equations 105 (1993), 46-62.
指導教授 許正雄(Cheng-hsiung Hsu) 審核日期 2008-6-20
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明