One-dimensional global attractor for the damped and driven sine-Gordon equation

被引：0
作者：
Min Qian
Shengfan Zhou
Shu Zhu
机构：
[1] Peking University,School of Mathematical Sciences
[2] Sichuan University,Department of Mathematics
来源：
Science in China Series A: Mathematics | 1998年 / 41卷
关键词：
sine-Gordon equation; global attractor; horizontal carve;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The damped and driven sine-Gordon equation with Neumann boundary conditions is studied. It is shown that it has a one-dimensional global attractor in a suitable functional space when the “damping” and the “diffusing” are not very small.
引用
收藏
页码：113 / 122
页数：9
相关论文
共 50 条
[31]   π-Kinks in the parametrically driven sine-Gordon equation and applications [J].
Mitkov, I ;
Zharnitsky, V .
PHYSICA D-NONLINEAR PHENOMENA, 1998, 123 (1-4) :301-307
[32]   Solutions of the three-dimensional sine-Gordon equation [J].
Aero, E. L. ;
Bulygin, A. N. ;
Pavlov, Yu. V. .
THEORETICAL AND MATHEMATICAL PHYSICS, 2009, 158 (03) :313-319
[33]   One-dimensional attractor for a strongly damped lattice system [J].
Hong-Yan, Li ;
Sheng-Fan, Zhou .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (06) :2702-2708
[34]   Solutions of the three-dimensional sine-Gordon equation [J].
E. L. Aero ;
A. N. Bulygin ;
Yu. V. Pavlov .
Theoretical and Mathematical Physics, 2009, 158
[35]   Control for the sine-Gordon equation [J].
Petcu, M ;
Temam, R .
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2004, 10 (04) :553-573
[36]   An ultradiscretization of the sine-Gordon equation [J].
Isojima, S ;
Murata, M ;
Nobe, A ;
Satsuma, J .
PHYSICS LETTERS A, 2004, 331 (06) :378-386
[37]   Numerical solution of one-dimensional nonlinear Sine-Gordon equation using LOOCV with exponential B-spline [J].
Rani, Richa ;
Arora, Geeta ;
Bala, Kiran .
COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (04)
[38]   On non-autonomous sine-Gordon type equations with a simple global attractor and some averaging [J].
Chepyzhov, VV ;
Vishik, MI ;
Wendland, WL .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2005, 12 (01) :27-38
[39]   GLOBAL ATTRACTOR FOR A ONE DIMENSIONAL WEAKLY DAMPED HALF-WAVE EQUATION [J].
Alouini, Brahim .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2021, 14 (08) :2655-2670
[40]   On the two-dimensional hyperbolic stochastic sine-Gordon equation [J].
Oh, Tadahiro ;
Robert, Tristan ;
Sosoe, Philippe ;
Wang, Yuzhao .
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2021, 268 (07) :2364-2376
12345