共查询到20条相似文献,搜索用时 15 毫秒
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当任意阶多项式增长的非线性项为耗散,且外力项仅属于L~2(Ω)时,研究了带衰退记忆的经典反应扩散方程的解在强拓扑空间H_0~1(Ω)×L_μ~2(R~+;D(A))的长时间行为.应用抽象函数理论、半群理论以及新的估计技巧,在拓扑空间H_0~1(Ω)×L_μ~2(R~+;D(A))上,验证了强解半群的渐近紧性并且证明了强全局吸引子的存在性. 相似文献
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当非线性项满足任意阶多项式增长且外力项仅属于H~(-1)(Ω)时,研究了带衰退记忆的经典反应扩散方程的长时间动力学行为.应用抽象函数理论、半群理论以及新的估计技巧,在空间L~2(Ω)×L_μ~2(R~+;H_0~1(Ω))上证明了全局吸引子的存在性.该结果改进和推广了Chepyzhov等人(2006)及Zhong等人(2006)的相应结果. 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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研究了具有双记忆项的非线性热弹耦合梁方程,利用已知的研究结果给出解的适定性定理,其次通过先验估计并结合常用不等式证明系统存在有界吸收集,且利用标准方法验证半群的渐近紧性,得到整体吸引子的存在性. 相似文献
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Glen Wheeler 《Journal of Mathematical Analysis and Applications》2011,375(2):685-698
We consider closed immersed hypersurfaces in R3 and R4 evolving by a special class of constrained surface diffusion flows. This class of constrained flows includes the classical surface diffusion flow. In this paper we present a Lifespan Theorem for these flows, which gives a positive lower bound on the time for which a smooth solution exists, and a small upper bound on the total curvature during this time. The hypothesis of the theorem is that the surface is not already singular in terms of concentration of curvature. This turns out to be a deep property of the initial manifold, as the lower bound on maximal time obtained depends precisely upon the concentration of curvature of the initial manifold in L2 for M2 immersed in R3 and additionally on the concentration in L3 for M3 immersed in R4. This is stronger than a previous result on a different class of constrained surface diffusion flows, as here we obtain an improved lower bound on maximal time, a better estimate during this period, and eliminate any assumption on the area of the evolving hypersurface. 相似文献
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本文证明了一类非线性发展方程全局解的存在性,并证明适当假设下,当非线性项满足临界指数增长条件时,方程具有紧吸引子。 相似文献
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We construct the trajectory attractor
of a three-dimensional Navier--Stokes system with exciting force
. The set
consists of a class of solutions to this system which are bounded in
, defined on the positive semi-infinite interval
of the time axis, and can be extended to the entire time axis
so that they still remain bounded-in-
solutions of the Navier--Stokes system. In this case any family of bounded-in-
solutions of this system comes arbitrary close to the trajectory attractor
. We prove that the solutions
are continuous in t if they are treated in the space of functions ranging in
. The restriction of the trajectory attractor
to
,
, is called the global attractor of the Navier--Stokes system. We prove that the global attractor
thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as
the trajectory attractors
and the global attractors
of the
-order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors
and
, respectively. Similar problems are studied for the cases of an exciting force of the form
depending on time
and of an external force
rapidly oscillating with respect to the spatial variables or with respect to time
. 相似文献
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Xuan Wang Lu Yang Chengkui Zhong 《Journal of Mathematical Analysis and Applications》2010,362(2):327-337
We discuss long-time dynamical behavior of the nonclassical diffusion equation with fading memory when nonlinearity is critical. The existence and regularity of global attractors in weak topological space and strong topological space are obtained, while the forcing term only belongs to H−1(Ω) and L2(Ω) respectively. The results in this part are new and appear to be optimal corresponding to the forcing term. 相似文献
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Bo-ling Guo Hai-yang HuangCenter of Nonlinear Studies Institute of Applied Physics Computational Mathematics. P.O. Box . Beijing ChinaDepartment of Mathematics. Beijing Normal University Beijing China 《应用数学学报(英文版)》2002,(4)
In this paper we consider the Burger-Ginzburg-Landau equations, and prove the existence of the global attractor in with finite Hausdorff and fractal dimensions. 相似文献
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主要研究了推广的Benjamin-Bona-Mahony(BBM)方程的解的渐近行为,通过证明半群的渐近紧性证明了方程在H)per2(Ω)中全局吸引子的存在性. 相似文献
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讨论了刻画层流问题中比重相近的层间相互作用的数学模型的初值问题.通过引进一类函数空间并证明该初值问题的解在所述空间上的一系列先验估计,得到了该初值问题在初值属于Hs(R)(s≥1)时的整体适定性. 相似文献
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非线性Sobolev-Galpern方程的有限维整体吸引子 总被引:5,自引:0,他引:5
本文研究非线性Sobolev-Galpern方程解的渐近性态.首先证明了该方程在H^2(Ω)∩H0^1(Ω)中整体弱吸引子的存在性,然后利用一个能量方程证明了整体弱吸引子实际上是整体强吸引子,建立了整体吸引子的有限维性. 相似文献
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黄海洋 《数学物理学报(A辑)》2002,22(3):316-322
文章通过对空间变量的有限差分方法离散了具有周期边值的Burgers Ginzburg Landau方程组.研究了这个离散方程组初值问题解的适定性.证明了当差分网格足够大时离散方程组存在吸引子,并得到了吸引子的Hausdorff维数和分形维数的上界估计.这个上界不会随着网格的加细而无限增大,因此数值分析离散的有限维系统的吸引子可以近似探讨原无限维系统的吸引子. 相似文献
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This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in˙ H 1 . 相似文献
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Shaohua Wu & Lei Liu 《偏微分方程(英文版)》2020,33(2):158-170
In this paper, we come up with a parabolic system modelling chemotaxis
with memory term, and establish the local existence and uniqueness of weak solutions.
The main methods we use are the fixed point theorem and semigroup theory. 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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In this paper, we study the asymptotic behavior of solutions for the partly dissipative lattice dynamical systems in weighted spaces. We first establish the dynamic systems on infinite lattice, and then prove the existence of the global attractor in weighted spaces by the asymptotic compactness of the solutions. It is shown that the global attractors contain traveling waves. The upper semicontinuity of the global attractor is also considered by finite-dimensional approximations of attractors for the lattice systems. 相似文献
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Chanyu Shang 《Journal of Mathematical Analysis and Applications》2008,343(1):1-21
This paper is concerned with the following one-dimensional nonlinear system of equations:
(0.1) 相似文献