共查询到19条相似文献,搜索用时 78 毫秒
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具有拟周期外力的非自治发展方程的惯性流形 总被引:1,自引:0,他引:1
本文主要研究了非自治发展方程的长时间性态,利用谱间断条件和广义雄性质,证明具有拟周期外 力的非自治发展方程的惯性流形的存在性,其惯性形式是具有拟周期外力的非自治有限维常微分方程. 特别对拟周期外力的反应扩散方程,证明了其惯性流形的存在性. 相似文献
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本文研究了二维无界区域上非自治Navier-Stokes方程的长时间行为.在外力项满足适当的条件下,证明了一致吸引子的存在性并给出了一致吸引子维数的上界估计. 相似文献
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该文首先介绍拉回渐近紧非自治动力系统的概念, 给出非自治动力系统拉回吸引子存在定理. 最后证明了无界区域上具线性阻尼的二维Navier-Stokes 方程的拉回吸引子的存在性, 并给出了其Fractal维数估计. 相似文献
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研究了有界区域上二维自治g-Navier-Stokes系统的双全局吸引子,利用非紧性测度方法,给出了一种验证其存在性的新方法.得出二维自治g-Navier-Stokes方程在有界区域上有一个非空、紧可逆H_g一V_g全局吸引子这一结论. 相似文献
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本文讨论非自治无穷维动力系统的解的长时间行为·在谱间隙条件成立的情况下,对一类非自治发展方程,我们构造了一族收敛的逼近惯性流形· 相似文献
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研究运动稳定性理论的新设想 总被引:2,自引:0,他引:2
本文提出一种研究稳定性的新设想,首先讨论了n维非自治系统,获得了其平凡解一致稳定、渐近稳定和不稳定的充分条件,然后讨论了n=2时,二维非自治系统和时变系数线性系统的稳定性,获得其平凡解一致稳定,渐近稳定和不稳定的充分条件。 相似文献
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The long-time behaviour of RungeKunge discretizationsis investigated when applied to a smooth nonautonomous index2 differential algebraic equation (DAE) with a cocycle structure,i.e. a DAE driven by an autonomous dynamical system, which isassumed to have a uniform attractor. It is shown that the cocyclestructure of the continuous dynamics is preserved under discretizationand that a uniform forward or pullback attractor of the DAEpersists under discretization by a RungeKutta schemewith the component subsets of the numerical attractor convergingupper semicontinuously to their continuous time counterparts. 相似文献
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Everaldo M. Bonotto Matheus C. Bortolan Tomás Caraballo Rodolfo Collegari 《Mathematical Methods in the Applied Sciences》2017,40(4):1095-1113
In this work, we define the notions of ‘impulsive non‐autonomous dynamical systems’ and ‘impulsive cocycle attractors’. Such notions generalize (we will see that not in the most direct way) the notions of autonomous dynamical systems and impulsive global attractors in the current published literature. We also establish conditions to ensure the existence of an impulsive cocycle attractor for a given impulsive non‐autonomous dynamical system, which are analogous to the continuous case. Moreover, we prove the existence of such attractor for a non‐autonomous 2D Navier–Stokes equation with impulses, using energy estimates. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Ahmed Y. Abdallah 《Journal of Differential Equations》2011,251(6):1489-1504
In Abdallah (2008, 2009) [2] and [3], we have investigated the existence of exponential attractors for first and second order autonomous lattice dynamical systems. Within this work, in l2, we carefully study the existence of a uniform exponential attractor for the family of processes associated with an abstract family of first order non-autonomous lattice dynamical systems with quasiperiodic symbols acting on a closed bounded set. 相似文献
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Lu Yang 《Nonlinear Analysis: Real World Applications》2012,13(3):1069-1079
We consider the dynamical behavior of the reaction-diffusion equation with nonlinear boundary condition for both autonomous and non-autonomous cases. For the autonomous case, under the assumption that the internal nonlinear term f is dissipative and the boundary nonlinear term g is non-dissipative, the asymptotic regularity of solutions is proved. For the non-autonomous case, we obtain the existence of a compact uniform attractor in H1(Ω) with dissipative internal and boundary nonlinearities. 相似文献
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John E. Franke James F. Selgrade 《Journal of Mathematical Analysis and Applications》2003,286(1):64-79
A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the union of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an autonomous map, properties that the nonautonomous attractor inherits from the autonomous attractor are discussed. Examples from population biology are presented. 相似文献
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Summary We consider a dynamical system described by an autonomous ODE with an asymptotically stable attractor, a compact set of orbitrary shape, for which the stability can be characterized by a Lyapunov function. Using recent results of Eirola and Nevanlinna [1], we establish a uniform estimate for the change in value of this Lyapunov function on discrete trajectories of a consistent, strictly stable multistep method approximating the dynamical system. This estimate can then be used to determine nearby attracting sets and attractors for the discretized system as done in Kloeden and Lorenz [3, 4] for 1-step methods.This work was supported by the U.S. Department of Energy Contract DE-A503-76 ER72012 相似文献
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本文首先给出了非自治随机动力系统的随机一致指数吸引子的概念及其存在性判据,其次证明了Rn上的带加法噪声和拟周期外力的FitzHugh-Nagumo系统的随机一致指数吸引子的存在性. 相似文献
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O.V. Kapustyan 《Journal of Mathematical Analysis and Applications》2011,373(2):535-547
In this paper we construct a dynamical process (in general, multivalued) generated by the set of solutions of an optimal control problem for the three-dimensional Navier-Stokes system. We prove the existence of a pullback attractor for such multivalued process. Also, we establish the existence of a uniform global attractor containing the pullback attractor. Moreover, under the unproved assumption that strong globally defined solutions of the three-dimensional Navier-Stokes system exist, which guaranties the existence of a global attractor for the corresponding multivalued semiflow, we show that the pullback attractor of the process coincides with the global attractor of the semiflow. 相似文献