共查询到20条相似文献,搜索用时 10 毫秒
1.
Rogério Martins 《Journal of Differential Equations》2005,212(2):351-365
Consider the attractor A of a periodically forced equation of pendulum type with linear friction, in the cylinder. Levi and independently Min, Xian and Jinyan show that if the friction coefficient is larger than a certain bound then A is homeomorphic to the circle. We shall give a topological version of the definition of inversely unstable solution of N. Levinson and show that the appearance of such solutions imply that A is not homeomorphic to the circle. As an application we shall show that the bounds on the friction coefficient obtained before are optimal. 相似文献
2.
In this paper the dynamical behaviors of a dispersive shallow water equation with viscosity, viscosity Degasperis–Procesi equation, are investigated. The existence of global solution to viscosity Degasperis–Procesi equation in L2 under the periodical boundary condition is studied and the existence of the global attractor of semi-group to solution on viscosity Degasperis–Procesi equation in H2 is obtained. 相似文献
3.
This paper aims to present a proof of the existence of the attractor for the one-dimensional viscous Fornberg–Whitham equation. In this paper, the global existence of solution to the viscous Fornberg–Whitham equation in L2 under the periodic boundary conditions is studied. By using the time estimate of the Fornberg–Whitham equation, we get the compact and bounded absorbing set and the existence of the global attractor for the viscous Fornberg–Whitham equation. 相似文献
4.
By the variable transformation and generalized Hirota method, exact homoclinic and heteroclinic solutions for Davey-Stewartson II (DSII) equation are obtained. For perturbed DSII equation, the existence of a global attractor is proved. The persistence of homoclinic and heteroclinic flows is investigated, and the special homoclinic and heteroclinic structure in attractors is shown. 相似文献
5.
The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system.Then we prove the random system possesses a global random attractor in H_0~1. 相似文献
6.
Roger J. Metzger Carlos A. Morales 《Bulletin of the Brazilian Mathematical Society》2006,37(1):89-101
Rovella proved the existence of measure-persistent attractors for flows exhibiting a unique singularity with three real eigenvalues
satisfying λ2 < λ3 < 0 < λ1 < −λ3 ([Ro]). In this paper we prove that most of them are in fact homoclinic classes.
*Partially supported by IMPA and CNPq.
**Partially supported by CNPq, FAPERJ and PRONEX/DYN-SYS. from Brazil. 相似文献
7.
Michele V. Bartuccelli 《Journal of Mathematical Analysis and Applications》2007,328(1):699-714
We consider a class of differential equations, , with ω∈Rd, describing one-dimensional dissipative systems subject to a periodic or quasi-periodic (Diophantine) forcing. We study existence and properties of trajectories with the same quasi-periodicity as the forcing. For g(x)=x2p+1, p∈N, we show that, when the dissipation coefficient is large enough, there is only one such trajectory and that it describes a global attractor. In the case of more general nonlinearities, including g(x)=x2 (describing the varactor equation), we find that there is at least one trajectory which describes a local attractor. 相似文献
8.
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
9.
ZHANG Rui-feng~ GUO Bo-ling~ Institute of Appl.Math. College of Math.and Inform.Sci. Henan Univ. Kaifeng China Institute of Appl.Phys.and Comput.Math. Beijing China. 《高校应用数学学报(英文版)》2008,23(1):57-64
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
10.
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
11.
The paper studies the longtime behavior of the Kirchhoff type equation with a strong dissipation utt−M(‖∇u‖2)Δu−Δut+h(ut)+g(u)=f(x). It proves that the related continuous semigroup S(t) possesses in the phase space with low regularity a global attractor which is connected. And an example is shown. 相似文献
12.
Fengjuan Meng Jie Wu Chunxiang Zhao 《Journal of Mathematical Analysis and Applications》2019,469(2):1045-1069
In this paper, we investigate the asymptotic behavior of the nonautonomous Berger equation on a bounded smooth domain with hinged boundary condition, where is a decreasing function vanishing at infinity. Under suitable assumptions, we establish an invariant time-dependent global attractor within the theory of process on time-dependent space. 相似文献
13.
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
14.
This work is devoted to the solvability and finite time blow-up of solutions of the Cauchy problem for the dissipative Boussinesq equation in all space dimension. We prove the existence and uniqueness of local mild solutions in the phase space by means of the contraction mapping principle. By establishing the time-space estimates of the corresponding Green operators, we obtain the continuation principle. Under some restriction on the initial data, we further study the results on existence and uniqueness of global solutions and finite time blow-up of solutions with the initial energy at three different level. Moreover, the sufficient and necessary conditions of finite time blow-up of solutions are given. 相似文献
15.
Xiaopeng Zhao 《Applicable analysis》2013,92(1):44-59
This article is concerned with a fourth-order parabolic equation. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the fourth-order parabolic equation possesses a global attractor in H k (0?≤?k?5) space, which attracts any bounded subset of H k (Ω) in the H k -norm. 相似文献
16.
In this paper, we study the longtime dynamics of the non‐autonomous Boussinesq‐type equation with critical nonlinearity, and time‐dependent external forcing, which is translation bounded but not translation compact. We prove the existence of a uniform attractor in . Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
17.
This paper is concerned with the attractor for a viscous two-component generalization of the Camassa-Holm equation subject to an external force, where the viscosity term is given by a second order differential operator. The global existence of solution to the viscous two-component Camassa-Holm equation with the periodic boundary condition is studied. We obtain the compact and bounded absorbing set and the existence of the global attractor in H2×H2 for the viscous two-component Camassa-Holm equation by uniform prior estimate and many inequalities. 相似文献
18.
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
19.
Olena Naboka 《Journal of Mathematical Analysis and Applications》2008,341(2):1107-1124
The dynamical system arising in the study of nonlinear oscillations of a number of coupled Berger plates is considered. The dependence of the long-time behavior of the trajectories of the system on the properties of the coupling operator is studied. It is shown that the global attractor of the dynamical system is continuous with respect to the coupling parameter γ expressing the intensity of plate interaction. When γ→∞ it converges upper semicontinuously to the attractor of the system generated by the projection of the vector field of the coupled system on the kernel of the coupling operator. For the particular case of 3-diagonal coupling operator the synchronization phenomenon at the level of attractors is stated for large values of γ as well as the absence of synchronization for γ small. The case of cluster synchronization is also considered. 相似文献
20.
Weike Wang 《Journal of Mathematical Analysis and Applications》2010,366(1):226-1008
In this paper, we study the global-in-time existence and the pointwise estimates of solutions to the Cauchy problem for the dissipative wave equation in multi-dimensions. Using the fixed point theorem, we obtain the global existence of the solution. In addition, the pointwise estimates of the solution are obtained by the method of the Green function. Furthermore, we obtain the Lp, 1?p?∞, convergence rate of the solution. 相似文献