Topological linearization of DEPCAGs with unbounded nonlinear terms

In this paper, we study the global topological linearization of a differential equation with piecewise constant argument of generalized type (DEPCAG) when the nonlinear term is unbounded. Some sufficient conditions are established for the topological conjugacy between a nonlinear system and its linear system. Our work generalizes the main result of Pinto and Robledo in [25].     

Successive Linearization Methods for Nonlinear Semidefinite Programs

We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Numerical results on some nonlinear semidefinite programs including optimization problems with bilinear matrix inequalities are reported to illustrate the behaviour of the proposed method.The research of the fourth author was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science. The research of the second author was supported by the DFG (Deutsche Forschungsgemeinschaft).     

全局线性化及同胚函数的■连续性

本文证明了微分方程全局线性化中的同胚函数及其逆同胚函数都具有连续性，同时给出了具体的估计式．     

一类含无界时滞的非线性系统的渐近稳定性

基于泛函微分方程的稳定性理论,首先通过构造Lyapunov泛函,再利用矩阵不等式的性质和范数的定义判定矩阵的正定性和负定性.对一类含无界时滞的非线性系统的渐近稳定性问题,作进一步的探讨.     

Global W2,p Solutions of GBBM Equations on Unbounded Domain

In this paper we study the initial boundary value problem of GBBM equations on unbounded domain u_t - Δu_t = div f(u) u(x,0) = u_0(x) u|_{∂Ω} = 0 and corresponding Cauchy problem. Under the conditions: f( s) ∈ C^sup1 and satisfies (H)\qquad |f'(s)| ≤ C|s|^ϒ, 0 ≤ ϒ ≤ \frac{2}{n-2} if n ≥ 3; 0 ≤ ϒ < ∞ if n = 2 u_0(x) ∈ W^{2,p}(Ω) ∩ W^{2,2}(Ω) ∩ W^{1,p}_0(Ω)(W^{2,p}(R^n) ∩ W^{2,2}(R^n) for Cauchy problem), 2 ≤ p < ∞, we obtain the existence and uniqueness of global solution u(x, t) ∈ W^{1,∞}(0, T; W^{2,p}(Ω) ∩ W^{2,2}(Ω) ∩ W^{1,p}_0(Ω))(W^{1,∞}(0, T; W^{2,p}(R^n) ∩ W^{2,2} (R^n)) for Cauchy problem), so the results of [1] and [2] are generalized and improved in essential.     

具有非线性热源项的耦合杆系统

主要以经典的算子半群理论为依据,研究了一类具有非线性热效应的耦合杆系统的长时间行为.首先在齐次边界条件和初始条件下,证明了系统解的存在唯一性;其次通过渐近先验估计,证明了系统有界吸收集的存在性;最后利用算子半群的分解技巧,得到了系统全局吸引子的存在性.     

二维无界区域中不可压非牛顿流体力学方程组的整体吸引子

研究一类二维无界区域中的等热双极不可压粘性非牛顿流体力学方程组，通过证明和相应的解半群的紧性，得到整体吸引子的存在性。     

临界情形下的全局拓扑线性化

非线性系ｘ＇＝Ａｘ＝ｆ（ｘ）线性化的基本条件是Ａ的特征根实部异于零．经典线性化的结论只限于原点小邻域［１］．后改进为全局性的［２,３］,但要求ｆ（ｘ）有界．在文［４］中我们去掉了ｆ（ｘ）有界的限制．本文将进一步去掉Ａ的特征根实部异于零的限制,证明了,只要ｆ（ｘ）有适当结构,全局线性化仍是可能的．     

一类平面三次向量场的全局拓扑结构

本文利用中心投影变换的思想证明了一类具有星形结点的平面三次向量场的几何性质依赖于无穷远处的几何性质.研究了该向量场的全局拓扑结构,得到了该向量场不考虑极限环的存在性时有27类不同的全局拓扑等价类,以及存在赤道闭轨线的充要条件和存在至少一个极限环的条件.     

A GENERALIZATION OF GLOBALLY TOPOLOGICAL LINEARIZATION THEOREM

In this paper, the globally topological linearization theorem of a certain system is given which generalizes the known result.     

具有非线性记忆项的耗散波动方程的整体吸引子

LetΩRn be a bounded domain with a smooth boundary.We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term utt+αut-△u-∫0t 0μ(t-s)|u(s)| βu(s)ds + g(u)=f.Based on a time-uniform priori estimate method,the existence of the compact global attractor is proved for this model in the phase space H10(Ω)×L2(Ω).     

非线性比式和问题的全局优化算法

In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1) that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained.The proposed algorithm is convergent to the global minimum of(P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Nume...     

无界区域中的非线性双曲型方程

本文研究无界区域中的非线性双曲方程u_tt+A2u+M(x,||A1/2u||₂2)Au=0这类问题的模型来自梁的横向挠曲方程.本文利用不动点方法结合能量估计证明了当M与x有关时,上述方程局部解的存在唯一性.     

一类带有三次项的平面五次微分系统的全局拓扑结构分析

一类带有三次项的平面五次微分系统在Poincare变换下可以讨论系统的无穷远奇点的性质,进而得到奇点附近轨线的拓扑结构,并利用判断函数给出极限环存在与否的条件,补充完善了五次系统的定性分析.     

可线性化非线性回归预测模型的剖析与改进

本文通过对可线性化非线性回归预测模型的剖析 ,得出了两个重要结论 .在此基础上 ,推导出了含有回归系数变化的可线性化非线性回归预测模型的一种有效改进方法——泰勒级数法 .最后 ,给出了一个应用实例     

GLOBAL LINEARIZATION OF DIFFERENTIAL EQUATIONS WITH SPECIAL STRUCTURES

This paper introduces the global linearization of the differential equations with special structures.The function in the differential equation is unbounded.We prove that the differential equation with unbounded function can be topologically linearlized if it has a special structure.     

Wintner定理的推广与全局光滑线性化

微分方程光滑线性化的研究,目前仅限于原点近傍的小邻域,本文给出了一个全局光滑线性化的结论.全局拓扑线性化或全局光滑线性化的先决条件是任一解的存在区间为全实轴.因此,本文也讨论了Wintner定理的推广问题.     

一类时变仿射非线性系统的完全线性化

本文用微分几何方法讨论时变仿射非线性系统的完全线性化问题 ,即同时线性化状态方程和输出方程 ,给出了一类时变仿射非线性系统完全线性化的充分条件     

Unbounded One-Dimensional Global Attractor for the Damped Sine-Gordon Equation

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