[1] Zhou Hua, Tang Jian,. Some properties and structures of solutionsof the swift-Hohenberg equation [J]. Journal of Southeast University (English Edition), 2003, 19 (3): 301-306. [doi:10.3969/j.issn.1003-7985.2003.03.020]

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Some properties and structures of solutionsof the swift-Hohenberg equation()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 3

Page:

301-306

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-09-30

Info

Title:

Some properties and structures of solutionsof the swift-Hohenberg equation

Author(s):

Zhou Hua¹;  Tang Jian²

¹Department of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
²Department of Mathematics, Nanjing University of Technology, Nanjing 210009, China

Keywords:

shooting technique;  Swift-Hohenberg equation;  critical point;  periodic solution

PACS:

O175.12

DOI:

10.3969/j.issn.1003-7985.2003.03.020

Abstract:

Stationary even periodic solutions of the Swift-Hohenberg equation are analyzed for the critical parameter k=1, and it is proved that there exist periodic solutions having the same energy as the constant solution u=0. For k≤ 0, some qualitative properties of the solutions are also proved.

References:

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[2] Bodenschatz E, Pesch W, Ahlers G. Recent developments in Rayleign-Bénard convection [J]. Ann Rev Fluid Mech, 2000, 32:709-778.
[3] Collet P, Eckmann J P. Instabilities and fronts in extended systems [J]. Princeton Series in Physics, 1990, 8(4):231-243.
[4] Cross M C, Hohenberg P C. Pattern formation outside of equilibrum [J]. Rev Mod Phys, 1993, 65(6): 851-1112.
[5] McLeod J B, Serrin J. The existence of similar solutions for some laminar boundary layer problems [J]. Arch Rational Mech Anal, 1968, 31(5): 288-303.
[6] Peletier L A, Troy W C. Spatial patterns described by the extended Fisher-Kolmogorov(EFK)equation: kinks [J]. Differential Integral Equations, 1995, 6(1): 1279-1304.
[7] Peletier L A, Troy W C. Spatial patterns described by the extended Fisher-Kolmogorov(EFK)equation: periodic solutions [J]. SIAM J Math Anal, 1997, 28(3): 1317-1353.
[8] Peletier L A, Troy W C. Chaotic solutions of the extended Fisher-Kolmogorov(EFK)equation [J]. J Differential Equations, 1996, 129(3): 458-508.
[9] Peletier L A, Troy W C. A topological shooting method and the existence of kinks of the extended Fisher-Kolmogorov equation [J]. Topol Methods Nonlinear Anal, 1996, 6(4): 331-355.
[10] Peletier L A, Troy W C. Multibump periodic travelling waves in suspension bridges [J]. Proc Roy Soc Edinburg, 1998, 128(2): 631-659.
[11] Peletier L A, Troy W C. Pattern formation described by the Swift-Hohenberg equation [A]. In: Research Institute for Mathematical Sciences ed. Proceedings of Kyoto[C]. Kyoto: Kyoto University, 2000.
[12] Tao Y, Zhang J. A shooting method for the Swift-Hohenberg equation [J]. Appl Math J Chinese Univ, Ser B, 2002, 17(4):391-403.
[13] Mizel V J, Peletier L A, Troy W C. Periodic phases in second-order materials [J]. Arch Rational Mech Anal, 1998, 145(4): 343-382.

Memo

Memo:

Biography: Zhou Hua(1965—), female, lecturer, zhoumo-nj@yahoo.com.cn.

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