共查询到20条相似文献,搜索用时 109 毫秒
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本文主要研究Neumann边界条件下带有周期外力的离散化强阻尼Sine-Gordon方程的全局吸引性.当摩擦系数足够大时,该系统将拥有一族周期解,这些周期解彼此之间只相差-个常向量的整数倍,并且该系统的任意一个解都将被其中的-个周期解所吸引. 相似文献
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非自治Ginzburg-Landau方程的周期解和全局周期吸引子 总被引:1,自引:0,他引:1
研究受周期外力影响的非自治Ginzburg-Landau方程的解的长时间行为.首先证明系统在空间H上存在周期解,而且周期解包含在空间V中的一个有界吸收集内.然后证明了当耗散系数λ满足一定条件时,该系统在空间H上具有唯一的周期解,该周期解指数吸引H中的任意有界集. 相似文献
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Duffing型方程组的边界值问题的解的存在性 总被引:5,自引:0,他引:5
给出了带Dirichlet边界条件、Neumann边界条件和周期边界条件的Duffing型方程组的两点边界值问题的解的几个存在性定理。 相似文献
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本文研究Ω(с)Rn(n=1,2,3)上具有几乎周期外力的非自治Ginzburg-Landau方程的有限维行为.证明了非自治Ginzburg-Landau系统存在紧的一致吸引子A1.当外力是时间拟周期时,得到了吸引子A1的Hausdorff维数的上界估计.当外力是时间周期时,证明了吸引子里一定含有周期解,而且当耗散系数λ满足适当条件时,系统在空间H=L2(Ω)上存在唯一周期解,该周期解指数吸引H中的任何有界集. 相似文献
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本文研究Ω R~n(n=1,2,3)上具有几乎周期外力的非自治Ginzburg-Landau方程的有限维行为。证明了非自治Ginzburg-Landau系统存在紧的一致吸引子A_1。当外力是时间拟周期时,得到了吸引子A_1的Hausdorff维数的上界估计,当外力是时间周期时,证明了吸引子里一定含有周期解,而且当耗散系数λ满足适当条件时,系统在空间H=L~2(Q)上存在唯一周期解,该周期解指数吸引H中的任何有界集。 相似文献
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本文主要研究一类带有齐次Neumann边界条件且具有非线性扩散项的趋化趋触模型,在较宽的条件下,证明了系统具有整体有界古典解.推广了XU等(2019)和JIA等(2020)得到的整体有界的古典解的结论. 相似文献
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Asymptotic synchronization in n-dimensional second order dissipative lattices of coupled oscillators
By introducing a new norm which is equivalent to the usual norm in the phase space, we prove that for n-dimensional second order dissipative lattices of coupled oscillators with external periodic forces under Dirichlet, Neumann and periodic boundary conditions, if the system is bounded dissipative and the coupled coefficients are both large enough, the asymptotic synchronization will occur. And we give a concrete bounded dissipative second order lattices system. Our results show that the bounds of the difference between the components of any solution are directly proportional to mn/2 and inversely proportional to the coupled coefficients, where m is the mesh size and n is the space dimension of lattice points. 相似文献
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In this paper, we investigate a coupled system of two Korteweg-de Vries equations on a bounded domain. We discuss the long-time behavior of this system with forces on the left Dirichlet boundary conditions. We obtain that if the forces are periodic (almost periodic) with small amplitude, then the solution of the coupled system is periodic (almost periodic). 相似文献
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Yanyan WANG 《Frontiers of Mathematics in China》2019,14(6):1339
For a coupled system of wave equations with Dirichlet boundary controls, this paper deals with the possible choice of its generalized synchronization matrices so that the admissible generalized exact boundary synchronizations for this system are obtained. 相似文献
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Canrong Tian 《Acta Appl Math》2011,113(2):195-206
In this paper, the two species Lotka-Volterra competition model of plankton allelopathy from aquatic ecology is discussed.
The authors study the existence of solutions to a strongly coupled elliptic system with homogeneous Dirichlet boundary conditions
and consider the existence, stability and global attractivity of time-periodic solutions for a coupled parabolic equations
in a bounded domain. Their results show that this model possesses at least one coexistence state if cross-diffusions and self-diffusions
are weak. The existence of the positive T-periodic solutions and the global stability as well as the global attractivity for
the parabolic system are also given. 相似文献
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Cecilia Cavaterra Alain Miranville 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2375-2399
We consider phase-field systems of Caginalp type on a three-dimensional bounded domain. The order parameter fulfills a dynamic boundary condition, while the (relative) temperature is subject to a homogeneous boundary condition of Dirichlet, Neumann or Robin type. Moreover, the two equations are nonlinearly coupled through a quadratic growth function. Here we extend several results which have been proven by some of the authors for the linear coupling. More precisely, we demonstrate the existence and uniqueness of global solutions. Then we analyze the associated dynamical system and we establish the existence of global as well as exponential attractors. We also discuss the convergence of given solutions to a single equilibrium. 相似文献
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M. Faierman 《Mathematische Nachrichten》2012,285(13):1643-1670
In this paper we consider a boundary problem for a parameter‐elliptic, multi‐order system of differential equations defined over a bounded region in $\mathbb {R}^n$ and under limited smoothness assumptions as well as under boundary conditions which include those of Dirichlet. Information is then derived concerning the asymptotic behaviour of the trace of a power of the resolvent of the Hilbert space operator, in general non‐selfadjoint, induced by the boundary problem under null boundary conditions. This information will then be used in a subsequent work to derive various results pertaining to the asymptotic behaviour of the eigenvalues of this operator. 相似文献
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From phenomena of synchronization to exact synchronization and approximate synchronization for hyperbolic systems 总被引:1,自引:0,他引:1
TaTsien Li 《中国科学 数学(英文版)》2016,59(1):1-18
In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations,and will be connected with the control theory via boundary controls in a finite time interval. More precisely,various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman's type are obtained. Finally, some prospects will be given. 相似文献
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E. A. Volkov 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):57-64
We study the Dirichlet problem for the Laplace equation in an infinite rectangular cylinder. Under the assumption that the
boundary values are continuous and bounded, we prove the existence and uniqueness of a solution to the Dirichlet problem in
the class of bounded functions that are continuous on the closed infinite cylinder. Under an additional assumption that the
boundary values are twice continuously differentiable on the faces of the infinite cylinder and are periodic in the direction
of its edges, we establish that a periodic solution of the Dirichlet problem has continuous and bounded pure second-order
derivatives on the closed infinite cylinder except its edges. We apply the grid method in order to find an approximate periodic
solution of this Dirichlet problem. Under the same conditions providing a low smoothness of the exact solution, the convergence
rate of the grid solution of the Dirichlet problem in the uniform metric is shown to be on the order of O(h
2 ln h
−1), where h is the step of a cubic grid. 相似文献
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We study a chemotaxis system on bounded domain in two dimensions where the formation of chemical potential is subject to the Dirichlet boundary condition. For such a system the solution is kept bounded near the boundary and hence the blowup set is composed of a finite number of interior points. If the initial total mass is 8π and the domain is close to a disc then the solution exhibits a collapse in infinite time of which movement is subject to a gradient flow associated with the Robin function. 相似文献
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Marek Galewski 《Applied Mathematics Letters》2011,24(12):2015-2018
We derive a dual variational method in order to obtain the existence of a bounded solution to a certain nonlinear system with non-monotone nonlinearities. We consider such a system representing a difference equation arising from evaluating some Dirichlet boundary value problems. 相似文献