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 共查询到19条相似文献,搜索用时 78 毫秒
1.
研究了一类非线性梁方程的渐近吸引子.即利用正交分解法构造一个有限维解序列.首先用数学归纳法证明了该解序列不会远离方程的整体吸引子,其次证明了它在长时间后无限趋于方程的整体吸引子,并给出了渐近吸引子的维数估计.  相似文献   

2.
具阻尼的KdV—KSV方程的整体吸引子   总被引:3,自引:0,他引:3  
夏红强 《应用数学》1999,12(1):31-36
本文证明了有阻尼的、没有Marangoni效应的KdV-KSV方程的周期初值问题存在整体吸引子,并且给出了该吸引子的Hausdorf维数和分形维数的上界估计  相似文献   

3.
Extended Fisher-Kolmogorov系统的渐近吸引子   总被引:1,自引:0,他引:1  
考虑了ExtendedFisher-Kolmogorov系统的解的长时间行为,构造了一个有限维解序列即该系统的渐近吸引子,证明了它在长时间后无限趋于方程的整体吸引子,并给出了渐近吸引子的维数估计.  相似文献   

4.
研究了 KdV-Burgers-Kuramoto 方程的渐近吸引子,即利用正交分解法构造一个有限维解序列。首先用数学归纳法证明了该解序列不会远离方程的整体吸引子,接着证明解序列在长时间后无限趋于方程的整体吸引子,最后给出渐近吸引子的维数估计。  相似文献   

5.
证明了具有弱阻尼项的广义KdV方程约周期初边值问题解的存在唯—性及整体吸引子存在性,最后获得了吸引子的Hausdorff维数和分形维数的上界估计.  相似文献   

6.
考虑二维有界多连通区域上具线性阻尼Navier-Stokes方程,在适当的边界条件下证明了解的存在唯一性及整体吸引子A的存在性,并给出了A的Hausdorff维数与Fractal维数.  相似文献   

7.
本文得到了一类具有线性阻尼且非线性项满足临界增长条件的非线性波动方程整体吸引子的Hausdorff维数、分形维数估计.  相似文献   

8.
带五次项的NLS方程及其谱逼近的整体吸引子的维数估计   总被引:1,自引:0,他引:1  
通过给出一般发展方程和其近似方程解的整体吸引子的Hausdorff维数上界间的关系,继[1,2]的讨论,本文进一步得到了带五次项的NLS方程和半离散Fourier谱近似解的整体吸引子的Hausdorff维数的上界估计。  相似文献   

9.
考虑了带有耗散项的Hasegawa-Mima方程解的长时间性态,研究了具有初值周期边值条件的Hasegawa-Mima方程的整体吸引子问题.运用关于时间的一致先验估计,证明了该问题整体吸引子的存在性,并获得了整体吸引子的维数估计.  相似文献   

10.
非线性波动与神经传播混合型方程的整体紧吸引子   总被引:1,自引:0,他引:1  
本文研究非线性波动与神经传播混合型方程u_tt=u_xxt+σ(u_x)_x-h(u)u_t-f(u)+g(x)初边值问题的整体吸引子.在σ∈C~2,σ'(s)>σo>0及h(s)∈C~1,-Co<)且∫~u_oh(s)sds>0)条件下我们得到了与该方程相应的动力系统整体紧吸引子的存在性,并证明了它具有有限的Hausdorff维数和fractal维数.  相似文献   

11.
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  
尚亚东  房少梅 《应用数学》2003,16(4):122-129
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   

12.
The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k.  相似文献   

13.
We prove local and global in time existence of non-negative weak solutions to the thin-film equation with absorption and obtain sufficient conditions for extra regularity of these solutions. Moreover, for the class of global strong solutions, we show existence of a trajectory attractor.  相似文献   

14.
This paper deals with the asymptotic behavior of solutions for the nonlinear Sobolev-Galpernequations.We first show the existence of the global weak attractor in H~2(Ω)∩H_0~1(Ω) for the equations.Andthen by an energy equation we prove that the global weak attractor is actually the global strong attractor.Thefinite-dimensionality of the global attractor is also established.  相似文献   

15.
We study the existence, uniqueness and continuous dependence on initial data of the solution for a nonlocal Cahn-Hilliard equation with Dirichlet boundary condition on a bounded domain. Under a nondegeneracy assumption the solutions are classical but when this is relaxed, the equation is satisfied in a weak sense. Also we prove that there exists a global attractor in some metric space.  相似文献   

16.
17.
1.IntroductionandMainResultsInthispaper,weconsiderthedampedsine-Gordonequation,withhomogeneousDirichletboundarycondition:whereu=u(x,t)ER,xEn,fiisaboundeddomaininRe(m=1,2,3)withsmoothboundaryoff,thedampingcoefficientor>0,thediffusingconstantd>0.Inthesequel,insteadofconsideringsystem(1.1),weinvestigatethefollowingsysteminHilbertspaceE=Ha(fi)xL'(fl):inwhichu(t)CHI(fl),v(t)6L'(fl)foranyt>0,A=--dA,G(u)=(--sine f),fEHa(~~),noEV.=Ha(~~),itoEH.=L'(fl).Let11'Onlayrwriteequatioll(l.2)asillwhi…  相似文献   

18.
In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with respect to two topologies—weak and strong. Each such system possesses a global attractor in the weak topology, but not necessarily in the strong. In case the latter exists and is weakly closed, it coincides with the weak global attractor. We give a sufficient condition for the existence of the strong global attractor, which is verified for the 3D NSE when all solutions on the weak global attractor are strongly continuous. We also introduce and study a two-parameter family of models for the Navier-Stokes equations, with similar properties and open problems. These models always possess weak global attractors, but on some of them every solution blows up (in a norm stronger than the standard energy one) in finite time.  相似文献   

19.
A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier–Stokes system coupled with a convective Cahn–Hilliard equation. In some recent contributions the standard Cahn–Hilliard equation has been replaced by its nonlocal version. The corresponding system is physically more relevant and mathematically more challenging. Indeed, the only known results are essentially the existence of a global weak solution and the existence of a suitable notion of global attractor for the corresponding dynamical system defined without uniqueness. In fact, even in the two-dimensional case, uniqueness of weak solutions is still an open problem. Here we take a step forward in the case of regular potentials. First we prove the existence of a (unique) strong solution in two dimensions. Then we show that any weak solution regularizes in finite time uniformly with respect to bounded sets of initial data. This result allows us to deduce that the global attractor is the union of all the bounded complete trajectories which are strong solutions. We also demonstrate that each trajectory converges to a single equilibrium, provided that the potential is real analytic and the external forces vanish.  相似文献   

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