BIFURCATIONS IN KURAMOTO-SIVASHINSKY EQUATIONS

被引：6
|
作者：
Kashchenko, S. A. [1 ,2 ]
机构：
[1] Demidov Yaroslavl State Univ, Yaroslavl, Russia
[2] Natl Res Nucl Univ MIFI, Moscow, Russia
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 2017年 / 192卷 / 01期
关键词：
bifurcation; stability; normal form; singular perturbation; dynamics; NONLINEAR STABILITY; DYNAMICAL PROPERTIES; WAVES; SYSTEMS; FILM;
D O I：
10.1134/S0040577917070029
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider the local dynamics of the classical Kuramoto-Sivashinsky equation and its generalizations and study the problem of the existence and asymptotic behavior of periodic solutions and tori. The most interesting results are obtained in the so-called infinite-dimensional critical cases. Considering these cases, we construct special nonlinear partial differential equations that play the role of normal forms and whose nonlocal dynamics thus determine the behavior of solutions of the original boundary value problem.
引用
收藏
页码：958 / 973
页数：16
相关论文
共 50 条
  • [41] Global Carleman estimates for the linear stochastic Kuramoto-Sivashinsky equations and their applications
    Gao, Peng
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 464 (01) : 725 - 748
  • [42] Stability of periodic Kuramoto-Sivashinsky waves
    Barker, Blake
    Johnson, Mathew A.
    Noble, Pascal
    Rodrigues, L. Miguel
    Zumbrun, Kevin
    APPLIED MATHEMATICS LETTERS, 2012, 25 (05) : 824 - 829
  • [43] INERTIAL MANIFOLDS FOR THE KURAMOTO-SIVASHINSKY EQUATION
    FOIAS, C
    NICOLAENKO, B
    SELL, GR
    TEMAM, R
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1985, 301 (06): : 285 - 288
  • [44] New bounds for the Kuramoto-Sivashinsky equation
    Giacomelli, L
    Otto, F
    COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2005, 58 (03) : 297 - 318
  • [45] A note on the Kuramoto-Sivashinsky equation with discontinuity
    D'Ambrosio, Lorenzo
    Gallo, Marco
    Pugliese, Alessandro
    MATHEMATICS IN ENGINEERING, 2021, 3 (05):
  • [46] Generalized solutions to the Kuramoto-Sivashinsky equation
    Biagioni, HA
    Iorio, RJ
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 1998, 6 (1-4) : 1 - 8
  • [47] Computational study of the Kuramoto-Sivashinsky equation
    Smyrlis, YS
    Papageorgiou, DT
    ADVANCES IN MULTI-FLUID FLOWS, 1996, : 426 - 432
  • [48] Scaling properties of the Kuramoto-Sivashinsky equation
    Li, J
    Sander, LM
    FRACTALS-AN INTERDISCIPLINARY JOURNAL ON THE COMPLEX GEOMETRY OF NATURE, 1995, 3 (03): : 507 - 514
  • [49] Feedback control of the Kuramoto-Sivashinsky equation
    Armaou, A
    Christofides, PD
    PHYSICA D, 2000, 137 (1-2): : 49 - 61
  • [50] Dynamical bifurcation for the Kuramoto-Sivashinsky equation
    Zhang, Yindi
    Song, Lingyu
    Axia, Wang
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (04) : 1155 - 1163
12345