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本文致力于讨论求解Kuramoto-Sivashinsky方程的非线性Galerkin方法,我们采用了sm个小尺度分量作反馈,并给出了收敛性结果,分析了误差估计.结论表明我们的修正方法是十分有效的. 相似文献
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N. A. Kudryashov 《Regular and Chaotic Dynamics》2008,13(3):234-238
The generalized Kuramoto-Sivashinsky equation in the case of the power nonlinearity with arbitrary degree is considered. New
exact solutions of this equation are presented.
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Kuramoto-Sivashinsky方程的B样条Galerkin方法 总被引:2,自引:0,他引:2
采用显隐结合的方法对微分算子进行时间离散 ,提出了解 Kuramoto-Sivashinsky方程的全离散 B样条 Galerkin方法 ,由此得到了有限元解的最优阶收敛性及稳定性估计 .最后的数值算例以图形的形式体现了此算法的精确度 相似文献
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在本文中,环状区域中的轴对称Kuramoto-Sivashinsky方程的有限维整体吸引子被得到了. 相似文献
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Claude-Michel Brauner 《数学研究》2016,49(2):93-110
In combustion theory, a thin flame zone is usually replaced by a free interface.
A very challenging problem is the derivation of a self-consistent equation for the
flame front which yields a reduction of the dimensionality of the system. A paradigm
is the Kuramoto-Sivashinsky (K-S) equation, which models cellular instabilities and
turbulence phenomena. In this survey paper, we browse through a series of models in
which one reaches a fully nonlinear parabolic equation for the free interface, involving
pseudo-differential operators. The K-S equation appears to be asymptotically the
lowest order of approximation near the threshold of stability. 相似文献
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We give a substantially simplified proof of the near-optimal estimate on the Kuramoto-Sivashinsky equation from a previous paper of the third author, at the same time slightly improving the result. That result relied on two ingredients: a regularity estimate for capillary Burgers and an a novel priori estimate for the inhomogeneous inviscid Burgers equation, which works out that in many ways the conservative transport nonlinearity acts as a coercive term. It is the proof of the second ingredient that we substantially simplify by proving a modified Kármán-Howarth-Monin identity for solutions of the inhomogeneous inviscid Burgers equation. We show that this provides a new interpretation of recent results obtained by Golse and Perthame. 相似文献
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Desheng Yang 《随机分析与应用》2013,31(6):1285-1303
Abstract Random systems may be more reasonable by incorporating influence of noise into deterministic systems. The notion of a random attractor is one of the very basic concepts of the theory of random dynamical systems. In this article, we consider the well-known Kuramoto–Sivashinsky equation with stochastic perturbation. Our aim is to attempt to obtain a so-called pull-back random attractor for stochastic Kuramoto–Sivashinsky equation. In particular, the Hausdorff dimension of a random attractor is finite. For simplicity, we always restrict ourselves to odd initial conditions, but the result for all initial conditions is also true. 相似文献
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用单调迭代法研究一类三阶微分方程边值问题解的存在性,不仅证明了该问题解的存在性,而且得到了其迭代格式. 相似文献
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Franco Obersnel Pierpaolo Omari 《Proceedings of the American Mathematical Society》2007,135(7):2055-2058
We extend a result of J. Andres and K. Pastor concerning scalar time-periodic first order ordinary differential equations without uniqueness, by proving that the existence of just one subharmonic implies the existence of large sets of subharmonics of all given orders. Since these periodic solutions must coexist with complicated dynamics, we might paraphrase T. Y. Li and J. A. Yorke by loosely saying that in this setting even period two implies chaos. Similar results are obtained for a class of differential inclusions.
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Yindi Zhang Lingyu SongWang Axia 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1155-1163
In this paper, by using the center manifold reduction method, together with the eigenvalue analysis, we made bifurcation analysis for the Kuramoto-Sivashinsky equation, and proved that the Kuramoto-Sivashinsky equation with constraint condition bifurcates an attractor Aλ as λ crossed the first critical value λ0=1 under the two cases. Our analysis was based on a new and mature attractor bifurcation theory developed by Ma and Wang (2005) [17] and [18]. 相似文献
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About the notion of non‐T‐resonance and applications to topological multiplicity results for ODEs on differentiable manifolds 下载免费PDF全文
By using topological methods, mainly the degree of a tangent vector field, we establish multiplicity results for T‐periodic solutions of parametrized T‐periodic perturbations of autonomous ODEs on a differentiable manifold M. In order to provide insights into the key notion of T‐resonance, we consider the elementary situations and . Doing so, we provide more comprehensive analysis of those cases and find improved conditions. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Felix Otto 《Journal of Functional Analysis》2009,257(7):2188-2245
In this paper, we consider solutions u(t,x) of the one-dimensional Kuramoto-Sivashinsky equation, i.e.
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A numerical technique based on the finite difference and collocation methods is presented for the solution of generalized Kuramoto-Sivashinsky (GKS) equation. The derivative matrices between any two families of B-spline functions are presented and are utilized to reduce the solution of GKS equation to the solution of linear algebraic equations. Numerical simulations for five test examples have been demonstrated to validate the technique proposed in the current paper. It is found that the simulating results are in good agreement with the exact solutions. 相似文献
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Jun-ying An Wei-guo Zhang 《应用数学学报(英文版)》2006,22(3):509-516
In this paper, we consider generalized BBM equation with nonlinear terms of high order.In the case of p=1/2, p=1 and p=2, the exact periodic solutions to G-BBM equation are obtained by means of proper transformation, which degrades the order of nonlinear terms. And we prove that if p ≠ 1/2,p ≠ 1 or p ≠ 2, G-BBM equation does not exist this kind of periodic solution. 相似文献
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针对东北师范大学微分方程教研室所编教材《常微分方程》中的一道例题,经过实际验算发现,原题所给向量函数并非如其所称是其所给微分方程组的基本解组;随后通过两种方法对该道例题给出正确求解. 相似文献