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耗散发展方程
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  dissipative evolution equations
     The attractors of a class of dissipative evolution equations which has a compact fractal structure be proved and such a structure is given also. Furthermore,an exponentially approximating sequence of compact fractal localizing sets of the attractor will be found out and the structure of attractor of the class of dissipative evolution equations be sharpened.
     证明了一类耗散发展方程的吸引子具有分形结构,并且给出了这一结构,进一步发现吸引子的指数逼近型紧分形局部化序列,这一结果精细了一类发展方程吸引子结构
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  “耗散发展方程”译为未确定词的双语例句
     In this paper we study the IBVP and the IVP for a class of evolution equations with nonlinear strong dissipation (1.1), and their multidimensional forms (4.1) with initial-boundary conditions (1.2) and (1.3) by means of the monotonicity method, the compactness method, the regularization method and their combination respectively.
     本文研究了一类非线性强耗散发展方程(1.1)和其多维形式(3.1)具初边值打件(0.2)和(0.3)的初边值问题和初值问题.
短句来源
     INITIAL-BOUNDARY VALUE PROBLEM AND INITIAL VALUE PROBLEM FOR A CLASS OF EVOLUTION EQUATIONS WITH NONLINEAR STRONG DISSIPATION
     一类非线性强耗散发展方程的初边值问题和初值问题(英文)
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     The Fractal Structure of the Attractors and Dissipative Evolution Equations
     耗散发展方程吸引子的分形结构(英文)
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     The results of F.
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     ON THR ECONOMIC DBVELOPMENT STRATEGY UNDER THE MODEL OF DISSIPATION STRUCTURE
     经济发展战略的耗散结构模式
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     The Fractal Structure of the Attractors and Dissipative Evolution Equations
     耗散发展方程吸引子的分形结构(英文)
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  dissipative evolution equations
We present a computational study evaluating the effectiveness of the nonlinear Galerkin method for dissipative evolution equations.
      
Many dissipative evolution equations possess a global attractor with finite Hausdorff dimension d.
      


In this paper we study the IBVP and the IVP for a class of evolution equations with nonlinear strong dissipation (1.1), and their multidimensional forms (4.1) with initial-boundary conditions (1.2) and (1.3) by means of the monotonicity method, the compactness method, the regularization method and their combination respectively. For the IBVP, suppose that σ_i(s) satisfy (H) and any one of (H_i) (1≤i≤4), and σ_i(s) satisfy (H)', (H_1)' (or(H_2)') and (H_5), we obtain the existence and uniqueness of the global...

In this paper we study the IBVP and the IVP for a class of evolution equations with nonlinear strong dissipation (1.1), and their multidimensional forms (4.1) with initial-boundary conditions (1.2) and (1.3) by means of the monotonicity method, the compactness method, the regularization method and their combination respectively. For the IBVP, suppose that σ_i(s) satisfy (H) and any one of (H_i) (1≤i≤4), and σ_i(s) satisfy (H)', (H_1)' (or(H_2)') and (H_5), we obtain the existence and uniqueness of the global strong solution for (1.1) and the global generalized solution for (4.1); for the IVP we obtain some similar results. So Prestel's results (1982) are improved and generalized.

本文研究了一类非线性强耗散发展方程(1.1)和其多维形式(3.1)具初边值打件(0.2)和(0.3)的初边值问题和初值问题.通过单调方法,紧致方法,正则化方法用它们之间的结合使用,对初边值问题,假设δ_i(s)满足(H)和(H_2)(1≤i≤4)中的任何一个,并且δ_i(s)满足(H),(H_1)',(或者(H_2)'及(H_5),我们得到(0.1)的整体强解和(3.1)的整体广义解的存在唯一性对初值问题,可得类似结果,从而Prestel的结果(1982)得到改进和推广.

In this paper the existence of inertial manifolds under time discretization for a class ofnonlinear evolution equation is discussed. It shows that if the time step h is sufficiently smalland the spectral gap condition for principle A is satisfied, then a simply difference scheme,corresponding to the evolution equation under discussion, possesses an inertial manifold Mh。This not only simplifies the proof of existence, but the theory can also be applied to moregeneral nonlinear terms, Moreover in this frame,it...

In this paper the existence of inertial manifolds under time discretization for a class ofnonlinear evolution equation is discussed. It shows that if the time step h is sufficiently smalland the spectral gap condition for principle A is satisfied, then a simply difference scheme,corresponding to the evolution equation under discussion, possesses an inertial manifold Mh。This not only simplifies the proof of existence, but the theory can also be applied to moregeneral nonlinear terms, Moreover in this frame,it is possible to construct a sequence of in-ertial manifolds {MhM}which tends to Mh as M→∞。

讨论了一类耗散发展方程时间离散化之后惯性流形的存在性,证明了如果时间步长充分小,且主算子A满足一个谱间隔条件,则所讨论的发展方程的一个简单差分格式存在一个惯性流形从,与DemengelF.的研究结果相比较,不仅简化了存在性证明,而且所建立的理论适用于更一般的非线性项,更进一步,在所建立的框架下,可以构造一个惯性流形序列{MhM},在某种意义下,当M→∞时,从MhM→Mh,当h趋于零时Mh的收敛性以及理论应用将在第Ⅱ部分讨论。

It has been proved that under some conditions there exists a fixed point Φ h for nonlinear inertial mapping T . Furthermore we obtained the graph of the Φ h which is an inertial manifold. In this paper the convergence of Φ h to Φ as h tends to zero is proved. Then as an example the theory is applied to the regularized Navier Stokes equations.

“发展方程的时间离散化惯性流形-Ⅰ”中已经证明了如果时间步长充分小,且主算子A满足谱间隔条件,则文中定义的一类耗散发展方程时间离散化的差分格式存在一个惯性流形Mh,它就是非线性映射T的不动点Φh∈Hb,l的图象.第Ⅱ部分继而证明了当h→0时,不动点Φh的收敛性.然后作为一个例子,把所建立的理论应用到正则化Navier-Stokes方程

 
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