共查询到20条相似文献,搜索用时 62 毫秒
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研究了周期边界条件下Kolmogorov-Spieqel-Sivashinsky方程的渐近吸引子,并给出了它的维数估计.首先利用正交分解法构造了一个有限维解序列,然后分两步证明该解序列收敛于方程的真实解. 相似文献
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Sine—Gordon方程的全局吸引子的维数估计 总被引:1,自引:0,他引:1
本文得到了阻尼Sine-Gordon方程的狄氏问题的全局吸引子的Hausdorff维数以偶数上界的参数条件,特别地,当阻尼与Laplae算子的第一个特征值适当大时,全局吸引子是零维的,零维吸引子恰是系统的唯一平衡解并且指数吸引相空间的有界集。 相似文献
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本文研究了一类二维非线性Schrodinger方程解的有限维行为,我们得到了此方程存在吸引子,并得到了此吸引子维数的上界估计 相似文献
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本研究了一类二维非线性Schrodinger方程解的有限维行为,我们得到了此方程存在吸引子,并得到了此吸引子维数的上界估计 相似文献
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一类带小参数反应——扩散型方程组的性态估计 总被引:6,自引:0,他引:6
得到了激光等离子能量交换模型研究中的一类反应--扩散方程组的本解的存在性。并通过引进光滑符号函数对解析解的性态进行了估计,为数值方法的误差分析提供了理论依据。 相似文献
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研究了无界区域Rn上Plate方程全局吸引子的正则性和有限分形维性.该方程的全局吸引子在相空间H2(Rn)×L2(Rn)的存在性已在先期文章建立,现在进一步证明该全局吸引子具有更好的正则性,即它是H4(Rn)×H2(Rn)的有界集并具有有限分形维数. 相似文献
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二维带形无界区域中Navier—Stokes方程整体吸引子及其维数估计 总被引:5,自引:0,他引:5
该文讨论二维无界带形区域中Navier-Stokes方程(Ⅰ){ut-△u+uiэuэxi=-△p+f(x,t)∈Ω×R+(1)divu=0(2)u(X,t)∈(H^10(Ω)for t〉0(3)u(x,0)=u0(x)∈H(4)其中Ω=(0,d)×R,d〉0为一常数,u与p为未知量,其中u=(u1,u2)为速度场,p表示压力。我们证明了当u0∈H,f∈V且f「log(e+│x│^2)」^12∈L 相似文献
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Yuncheng You 《Journal of Applied Analysis & Computation》2016,6(4):1000-1022
Asymptotic pullback dynamics of a typical stochastic reaction-diffusion system, the reversible Schnackenberg equations, with multiplicative white noise is investigated. The robustness of random attractor with respect to the reverse reaction rate as it tends to zero is proved through the uniform pullback absorbing property and the uniform convergence of reversible to non-reversible cocycles. This result means that, even if the reverse reactions would be neglected, the dynamics of this class of stochastic reversible reaction-diffusion systems can still be captured by the random attractor of the non-reversible stochastic raction-diffusion system in a long run. 相似文献
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反应扩散方程古典解的最大吸引子 总被引:1,自引:0,他引:1
利用能量积分和解析半群的有关估计,一类反应扩散方程非负古典解在连续函数空间的最大吸引子的存在性被证明,且非线性项取为任意阶多项式. 相似文献
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The long-time dynamical behavior of the non-autonomous nonclassical diffusion equation with fading memory, when nonlinearity is critical, is discussed for in the weak topological space . First, the asymptotic regularity of solutions is proven, and then the existence of a compact uniform attractor together with its structure and regularity is obtained, while the time-dependent forcing term is only translation bounded instead of translation compact. The result extends and improves some results given in [Y. Xiao, Attractors for a nonclassical diffusion equation, Acta Math. Appl. Sin. Engl. Ser. 18 (2002) 273–276; C. Sun, M. Yang, Dynamics of the nonclassical diffusion equations, Asympt. Anal. 59 (2008) 51–81]. 相似文献
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Attractors for a Nonclassical Diffusion Equation 总被引:11,自引:0,他引:11
Yue-long XiaoDepartment of Mathematics Xiangtan University Xiangtan China 《应用数学学报(英文版)》2002,18(2):273-276
Abstract For a nonclassical diffusion equation,the asymptotic behavior is investigated,and the existence ofa global attractor is proved. 相似文献
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Alain Miranville 《Applications of Mathematics》2003,48(1):31-47
In this article we introduce the notion of a minimal attractor for families of operators that do not necessarily form semigroups. We then obtain some results on the existence of the minimal attractor. We also consider the nonautonomous case. As an application, we obtain the existence of the minimal attractor for models of Cahn-Hilliard equations in deformable elastic continua. 相似文献
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This paper is concerned with the existence of maximal attractors in Hi (i = 1, 2,4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn(n = 2,3). 相似文献
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Global Attractors for a Nonclassical Diffusion Equation 总被引:4,自引:0,他引:4
Chun You SUN Su Yun WANG Cheng Kui ZHONG 《数学学报(英文版)》2007,23(7):1271-1280
We prove the existence of global attractors in H0^1 (Ω) for a nonclassical diffusion equation. Two types of nonlinearity f are considered: one is the critical exponent, and the other is the polynomial growth of arbitrary order. 相似文献
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In this paper we study the existence of pullback global attractors for multivalued processes generated by differential inclusions. First, we define multivalued dynamical processes, prove abstract results on the existence of -limit sets and global attractors, and study their topological properties (compactness, connectedness). Further, we apply the abstract results to nonautonomous differential inclusions of the reaction–diffusion type in which the forcing term can grow polynomially in time, and to stochastic differential inclusions as well. 相似文献
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对由一类非线性抛物型变分不等方程所描述的无穷维动力系统,给出了存在全局吸引子及弱近似惯性流形的充分条件. 相似文献
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The paper deals with infinite-dimensional random dynamical systems. Under the condition that the system in question is of mixing type and possesses a random compact attracting set, we show that the support of the unique invariant measure is the minimal random point attractor. The results obtained apply to the randomly forced 2D Navier–Stokes system. 相似文献