共查询到19条相似文献,搜索用时 93 毫秒
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In this paper,we consider the strong dissipative KDV type equation on an unbounded domain R1.By applying the theory of decomposing operator and the method of constructing some compact operator in weighted space,the existence of exponential attractor in phase space H2(R1) is obtained. 相似文献
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This paper is concerned with the three-dimensional non-autonomous BrinkmanForchheimer equation.By Galerkin approximation method,we give the existence and uniqueness of weak solutions for non-autonomous Brinkman-Forchheimer equation.And we investigate the asymptotic behavior of the weak solution,the existence and structures of the(H,H)-uniform attractor and(H,V)-uniform attractor.Then we prove that an L 2-uniform attractor is actually an H 1-uniform attractor. 相似文献
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本文研究具有记忆项和非局部非线性项的板方程.首先利用近似的Faedo-Galerkin方法证得方程在初边值条件下解的适定性定理;其次通过先验估计并结合常用不等式证明该系统存在有界吸收集;最后利用Sobolev紧嵌入和收缩函数的方法证得解半群的渐近紧性,从而得到该系统整体吸引子的存在性. 相似文献
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The initial boundary value problem for the fourth-order wave equation utt △2u u=|t|p-1u is considered.The existence and uniqueness of global weak solutions is obtained by using the Galerkin method and the concept of stable set due to Sattinger. 相似文献
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当非线性项以任意阶多项式增长,且外力项仅为平移有界而非平移紧时,研究了非自治经典反应扩散方程解的长时间动力学行为.应用抽象函数理论和新的估计技术,在拓扑空间L~2(Ω)×L_μ~2(R~+;H_0~1(Ω)上,证明了一致吸引子的存在性.该结果改进和推广了Chepyzhov等(2006)和钟承奎等(2006)的相应结果. 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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本文讨论了一类带调和势|x|^2的非线性Schroedinger方程解的长时间行为,证明了整体吸引子的存在性. 相似文献
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本文主要考虑齐次Neumann边界条件下强阻尼波动方程的全局吸引子的存在性.利用渐近时间周期微分方程的极限集的性质,证明了在一定的参数范围内,齐次Neumann边界条件下强阻尼波动方程存在一维全局吸引子,是一条水平曲线. 相似文献
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本文主要考虑齐次Neumann边界条件下强阻尼波动方程的全局吸引子的存在性.利用渐近时间周期微分方程的极限集的性质,证明了在一定的参数范围内,齐次Neumann边界条件下强阻尼波动方程存在一维全局吸引子,是一条水平曲线. 相似文献
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Hong-yan Li Sheng-fan Zhou 《应用数学学报(英文版)》2006,22(1):75-80
In this paper we consider the strongly damped and driven nonlinear wave equations under homogeneous Dirichlet boundary conditions. By introducing a new norm which is equivalent to the usual norm, we obtain the existence of a global periodic attractor attracting any bounded set exponentially in the phase space, which implies that the system behaves exactly as a one dimensional system. 相似文献
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研究了一类非线性蜕化方程。引入带权L^2空间,证明了方程初边值问题整体解的存在唯一性,并在无穷维空间证明了(E0,E)型整体吸引子的存在性。 相似文献
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Summary. The dynamical behavior of the damped sine-Gordon equation with homogeneous Neumann boundary condition is studied. It is shown
that the equation has an unbounded one-dimensional global attractor in a suitable functional space when the ``damping' and
the ``diffusing' are not very small.
Received March 16, 1999; accepted December 10, 1999 相似文献
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1 IntroductionIn this paper we study globaJ solutions to the initiaLboundary value prob1em for quasilinearwave equations with viscosity and a nonlinear perterbation of the fOrmwhere fl is a bounded domain in RN with smooth boundarY afl, and the norilineax termsa(vp), g(u) axe like a(vp) = (l + )vlP)--'/P(P > 1), g(u) =--ju1"u.This problem describes the motion of fixed membrane with strong viscosity. The globalexistence and stability Of smooth solutions fOr one space dimensional case N = 1… 相似文献
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Random Attractor for Non-autonomous Stochastic Strongly Damped Wave Equation on Unbounded Domains 下载免费PDF全文
In this paper we study the asymptotic dynamics for the nonautonomous stochastic strongly damped wave equation driven by additive noise defined on unbounded domains. First we introduce a continuous cocycle for the equation and then investigate the existence and uniqueness of tempered random attractors which pullback attract all tempered random sets. 相似文献
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我们考虑如下方程的整体解的存在性:uxt 3/2ux^2uxx Uxxxx-sinu εux=f我们先给出了一致性先验估计,然后在H0^1∩H^2空间证明了整体解的存在性. 相似文献
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强阻尼波动方程吸引子的正则性及其逼近 总被引:1,自引:0,他引:1
该文研究强阻尼波动方程的初边值问题.利用线性主算子在相空间中生成的解析半群的性质,证明了解的光滑效应,这个现象与弱阻尼波动方程的情形大不相同.由此作者得到了吸引子的正则性,并象自伴情形那样构造了近似惯性流形. 相似文献