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Dynamical bifurcation of the two dimensional Swift-Hohenberg equation with odd periodic condition
1. | Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, 1 Hoegi-Dong, Dongdaemun-Gu, Seoul, 130-701, South Korea |
2. | Department of Mathematics, National Taiwan University, Taipei, 10617 |
References:
[1] |
I. S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equations,, Rev. Mod. Phys., 74 (2002), 99.
doi: 10.1103/RevModPhys.74.99. |
[2] |
M. C. Cross and P. C. Hohenberg, Pattern formation outside of equillibrium,, Rev. Mod. Phys., 65 (1993), 851.
doi: 10.1103/RevModPhys.65.851. |
[3] |
S. Day, Y. Hiraoka, K. Mischaikow and T. Ogawa, Rigorous numerics for global dynamics: A study of the Swift-Hohenberg equationm,, SIAM J. Appl. Dyn. Sys., 4 (2005), 1.
|
[4] |
J. P. Gollub and J. S. Langer, Pattern formation in nonequilibrium physics,, Rev. Mod. Phys., 71 (1999), 396.
doi: 10.1103/RevModPhys.71.S396. |
[5] |
J. Han and M. Yari, Dynamic bifurcation of the one-dimensional periodic Swift-Hohenberg equation,, Bull. Korean Math. Soc., (). Google Scholar |
[6] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,", Lecture Notes in Mathematics, 840 (1981).
|
[7] |
T. Ma and S. Wang, "Bifurcation Theory and Applications,", World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 53 (2005).
|
[8] |
T. Ma and S. Wang, "Phase Transition Dynamics in Nonlinear Sciences,", Springer, (). Google Scholar |
[9] |
L. A. Peletier and, V. Rottschäfer, Pattern selection of solutions of the Swift-Hohenberg equation,, Physica D, 194 (2004), 95.
doi: 10.1016/j.physd.2004.01.043. |
[10] |
L. A. Peletier and W. C. Troy, "Spatial Patterns: Higher Order Models in Physics and Mecahnics,", Progress in Nonlinear Differential Equations and their Applications, 45 (2001).
|
[11] |
L. A. Peletier and J. F. Williams, Some canonical bifurcations in the Swift-Hohenberg equation,, SIAM J. Appl. Dyn. Sys., 6 (2007), 208.
|
[12] |
J. Swift and P. C. Hohenberg, Hydrodynamic fluctuations at the convective instability,, Phys. Rev. A, 15 (1977), 319.
doi: 10.1103/PhysRevA.15.319. |
[13] |
M. Yari, Attractor bifurcation and final patterns of the n-dimensional and generalized Swift-Hohenberg equations,, Dis. Cont. Dyn. Sys. Ser. B, 7 (2007), 441.
|
show all references
References:
[1] |
I. S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equations,, Rev. Mod. Phys., 74 (2002), 99.
doi: 10.1103/RevModPhys.74.99. |
[2] |
M. C. Cross and P. C. Hohenberg, Pattern formation outside of equillibrium,, Rev. Mod. Phys., 65 (1993), 851.
doi: 10.1103/RevModPhys.65.851. |
[3] |
S. Day, Y. Hiraoka, K. Mischaikow and T. Ogawa, Rigorous numerics for global dynamics: A study of the Swift-Hohenberg equationm,, SIAM J. Appl. Dyn. Sys., 4 (2005), 1.
|
[4] |
J. P. Gollub and J. S. Langer, Pattern formation in nonequilibrium physics,, Rev. Mod. Phys., 71 (1999), 396.
doi: 10.1103/RevModPhys.71.S396. |
[5] |
J. Han and M. Yari, Dynamic bifurcation of the one-dimensional periodic Swift-Hohenberg equation,, Bull. Korean Math. Soc., (). Google Scholar |
[6] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations,", Lecture Notes in Mathematics, 840 (1981).
|
[7] |
T. Ma and S. Wang, "Bifurcation Theory and Applications,", World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, 53 (2005).
|
[8] |
T. Ma and S. Wang, "Phase Transition Dynamics in Nonlinear Sciences,", Springer, (). Google Scholar |
[9] |
L. A. Peletier and, V. Rottschäfer, Pattern selection of solutions of the Swift-Hohenberg equation,, Physica D, 194 (2004), 95.
doi: 10.1016/j.physd.2004.01.043. |
[10] |
L. A. Peletier and W. C. Troy, "Spatial Patterns: Higher Order Models in Physics and Mecahnics,", Progress in Nonlinear Differential Equations and their Applications, 45 (2001).
|
[11] |
L. A. Peletier and J. F. Williams, Some canonical bifurcations in the Swift-Hohenberg equation,, SIAM J. Appl. Dyn. Sys., 6 (2007), 208.
|
[12] |
J. Swift and P. C. Hohenberg, Hydrodynamic fluctuations at the convective instability,, Phys. Rev. A, 15 (1977), 319.
doi: 10.1103/PhysRevA.15.319. |
[13] |
M. Yari, Attractor bifurcation and final patterns of the n-dimensional and generalized Swift-Hohenberg equations,, Dis. Cont. Dyn. Sys. Ser. B, 7 (2007), 441.
|
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