Bifurcations in Kuramoto–Sivashinsky equations

被引：0

作者：

S. A. Kashchenko

机构：

[1] Demidov Yaroslavl State University,

[2] National Research Nuclear University “MIFI,undefined

[3] ”,undefined

来源：

Theoretical and Mathematical Physics | 2017年 / 192卷

关键词：

bifurcation; stability; normal form; singular perturbation; dynamics;

D O I：

暂无

中图分类号：

学科分类号：

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

页码：958 / 973

页数：15

共 50 条

[21] New exact solutions and conservation laws of a class of Kuramoto Sivashinsky (KS) equations [J].

Govinder, K. S. ;

Narain, R. ;

Okeke, J. E. .

QUAESTIONES MATHEMATICAE, 2019, 42 (01) :93-112

[22] Bifurcations and Patterns in the Kuramoto Model with Inertia [J].

Chiba, Hayato ;

Medvedev, Georgi S. ;

Mizuhara, Matthew S. .

JOURNAL OF NONLINEAR SCIENCE, 2023, 33 (05)

[23] From the Kuramoto-Sakaguchi model to the Kuramoto-Sivashinsky equation [J].

Kawamura, Yoji .

PHYSICAL REVIEW E, 2014, 89 (01)

[24] Long time stability of nonlocal stochastic Kuramoto-Sivashinsky equations with jump noises [J].

Wang, Guanying ;

Wang, Xingchun ;

Xu, Guangli .

STATISTICS & PROBABILITY LETTERS, 2017, 127 :23-32

[25] The asymptotic behavior of the stochastic coupled Kuramoto-Sivashinsky and Ginzburg-Landau equations [J].

Lin, Lin ;

Li, Mei .

BOUNDARY VALUE PROBLEMS, 2020, 2020 (01)

[26] On the controllability of a system coupling Kuramoto-Sivashinsky-Korteweg-de Vries and transport equations [J].

Kumar, Manish ;

Majumdar, Subrata .

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2024, 36 (04) :875-926

[27] Bifurcation of two-dimensional Kuramoto-Sivashinsky equation [J].

Li C.P. ;

Yang Z.H. .

Applied Mathematics-A Journal of Chinese Universities, 1998, 13 (3) :263-270

[28] Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations [J].

Xu, Yan ;

Shu, Chi-Wang .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 195 (25-28) :3430-3447

[29] COMPUTATIONAL STUDY OF THE DISPERSIVELY MODIFIED KURAMOTO-SIVASHINSKY EQUATION [J].

Akrivis, G. ;

Papageorgiou, D. T. ;

Smyrlis, Y. -S. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (02) :A792-A813

[30] On the Global Existence for the Kuramoto-Sivashinsky Equation [J].

Kukavica, Igor ;

Massatt, David .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2023, 35 (01) :69-85

← 1 2 3 4 5 →