Derivation of a model of nonlinear micropolar plate

In this paper we derive a two-dimensional model of nonlinear micropolar plate. We start from the equilibrium problem for the three-dimensional nonlinear micropolar elastic plate-like body with nonlinear strains and linear constitutive law. Using the asymptotic expansion we formally derive the two-dimensional problem, posed on the middle plane of the plate-like body, for the leading deformation and microrotation.      

非线性弹性杆振动方程的全局吸引子及正则性

证明了非线性弹性杆振动方程全局吸引子的正则性,并进一步获得了(H_0~1(Ω)×H_0~1(Ω),(H~2(Ω)∩H_0~1(Ω))×(H~2(Ω)∩H_0~1(Ω)))-全局吸引子的存在性.     

Blowup and Asymptotic Behavior of a Free Boundary Problem with a Nonlinear Memory

In this paper, we investigate a reaction-diffusion equation $u_t-du_{xx}=au+\int_{0}^{t}u^p(x,\tau){\rm d}\tau+k(x)$ with double free boundaries. We study blowup phenomena in finite time and asymptotic behavior of time-global solutions. Our results show if $\int_{-h_0}^{h_0}k(x)\psi_1 {\rm d}x$ is large enough, then the blowup occurs. Meanwhile we also prove when $T^*<+\infty$, the solution must blow up in finite time. On the other hand, we prove that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial datum is small sufficiently.     

Asymptotic Behavior of a Class of Nonlinear Delay Difference Equations

In this paper, we shall study the asymptotic behavior of solutions of difference equations of the form x n +1 = x n p f ( x n m k 1 , x n m k 2 ,…, x n m k r ), n =0,1,…, where p is a positive constant and k 1 ,…, k r are (fixed) nonnegative integers. In particular, permanence and global attractivity will be discussed.     

杆,壳理论在Hilbert空间的构造

本文在Hilbert空间这一数学框架下系统地构造了杆、壳的一般理论,并成功地获得了对该理论系统的误差估计.     

两参数反应扩散方程解的渐近性态

本文讨论了一类具有双参数的反应扩散方程初始边值问题.利用微分不等式理论,研究了初始边值问题解的渐近性态.     

具反应梯度项的多重非线性抛物方程解的渐近行为

对一类具非线性内吸收、反应梯度项及边界流的半线性抛物方程,研究了更加困难的临界情形下的爆破解的渐近行为,填补了先前工作遗留的缺口.为此,引入了改进的伸缩变换方法.     

一类广义非线性Euler-Poisson-Darboux方程整体解的渐近性质

W.A.Strauss等人已证明了广义非线性 Euler-Poisson-Darboux方程初边值问题整体解的存在唯一性 .本文应用一个差分不等式研究了整体解的渐近性质 .     

三阶非线性中立型变时滞动力方程的渐近性与振动性(英文)

考虑了时标上三阶非线性中立型变时滞动力方程的渐近性和振动性.利用广义Ric-cati技巧与完全平方技巧,获得了方程所有解渐近和振动的准则.所得结果推广了已有三阶动力方程的结果,给出了一些例子加以说明本文的主要结论.     

Asymptotic Zero Behavior of Laguerre Polynomials with Negative Parameter

We consider Laguerre polynomials $L_n^{(\alpha_n)}(nz)$ with varying negative parameters $\alpha_n$, such that the limit $A = -\!\lim_n \alpha_n/n$ exists and belongs to $(0,1)$. For $A > 1$, it is known that the zeros accumulate along an open contour in the complex plane. For every $A \in (0,1)$, we describe a one-parameter family of possible limit sets of the zeros. Under the condition that the limit $r= - \!\lim_n {1}/{n} \log [\dist\!(\alpha_n, \mbox{\footnotesize{\bf Z}})]$ exists, we show that the zeros accumulate on $\Gamma_r \cup [\beta_1,\beta_2]$ with $\beta_1$ and $\beta_2$ only depending on $A$. For $r \in [0,\infty)$, $\Gamma_r$ is a closed loop encircling the origin, which for $r = +\infty$, reduces to the origin. This shows a great sensitivity of the zeros to $\alpha_n$s proximity to the integers. We use a Riemann–Hilbert formulation for the Laguerre polynomials, together with the steepest descent method of Deift and Zhou to obtain asymptotics for the polynomials, from which the zero behavior follows.     

三阶非线性微分方程解的渐近性

建立了三阶非线性微分方程…x+φ(x,x.,¨x)¨x+f(x,x.)=p(t,x,x.,¨x)的一切解有界和收敛到零的充分条件.     

Asymptotic analysis of an elastic rod with rounded ends

We derive a one-dimensional model for an elastic shuttle, that is, a thin rod with rounded ends and small fixed terminals, by means of an asymptotic procedure of dimension reduction. In the model, deformation of the shuttle is described by a system of ordinary differential equations with variable degenerating coefficients, and the number of the required boundary conditions at the end points of the one-dimensional image of the rod depends on the roundness exponent m∈(0,1). Error estimates are obtained in the case m∈(0,1/4) by using an anisotropic weighted Korn inequality, which was derived in an earlier paper by the authors. We also briefly discuss boundary layer effects, which can be neglected in the case m∈(0,1/4) but play a crucial role in the formulation of the limit problem for m ≥ 1/4.     

The Asymptotic Behavior of Solutions of Some Doubly Degenerate Nonlinear Parabolic Equations

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Asymptotic behavior of a nonlinear delay difference equation

This paper considers a class of nonlinear difference equations

Δ₃y_n + ƒ(n, y_n, y_n−r) = 0, n N (n₀)

. A necessary and sufficient condition for the existence of a bounded nonoscillatory solution is given.     

具强迫项非线性梁方程解的渐近性

本文同时考虑纵横弯曲及粘性效应,建立了一类轴向载荷和横向载荷作用下的非线性粘弹性简支梁方程。利用Faedo-Galerkin法,证明了该方程解的存在唯一性,讨论了该方程解的渐近性,并给出了有界吸收集的存在性证明。     

一类非线性中立型系统的渐近稳定性

基于李雅普诺夫泛函方法,本文讨论了一类非线性中立型系统渐近稳定性的充分条件,推广了中立型系统稳定性结果。最后,通过实例及其仿真数值模拟验证了上述理论结果。     

在局部区域上的奇摄动非线性方程Robin边值问题解的渐近性态

本文是讨论了一类在局部区域上的奇摄动非线性方程Ｒobin边值问题,利用泛函数分析及算子理论,得到了相应问题解的渐近性态。     

Asymptotic behaviour of curved rods by the unfolding method

We consider in this work general curved rods with a circular cross‐section of radius δ. Our aim is to study the asymptotic behaviour of such rods as δ→0, in the framework of the linear elasticity according to the unfolding method. It consists in giving some decompositions of the displacements of such rods, and then in passing to the limit in a fixed domain. A first decomposition concerns the elementary displacements of a curved rod which characterize its translations and rotations, and the residual displacements related to the deformation of the cross‐section. The second decomposition concerns the displacements of the middle‐line of the rod. We prove that such a displacement can be written as the sum of an inextensional displacement and of an extensional one. An extensional displacement will modify the length of the middle‐line, while an inextensional displacement will not change this length in a first approximation. We show that the H¹‐norm of an inextensional displacement is of order 1, while that of an extensional displacement is in general, of order δ. A priori estimates are established and convergence results as δ→0, are given for the displacements. We give their unfolded limits, as well as the unfolded limits of the strain and stress tensors. To prove the convergence of the strain tensor, the introduction of elementary and residual displacements appears as essential. By passing to the limit as δ→0 in the linearized system of the elasticity, we obtain on the one hand, a variational problem that is satisfied by the limit extensional displacement, and on the other hand, a variational problem coupling the limit of inextensional displacements and the limit of the angle of torsion. Copyright © 2004 John Wiley & Sons, Ltd.     

联合载荷作用下压杆稳定性分析

利用数学分析的基本知识建立了联合载荷作用下压杆的一般控制方程.基于两点边值问题的打靶法计算了悬臂梁在某些特定联合载荷作用下的后屈曲载荷.通过与T im oshenko用椭圆积分法所得结果进行比较,证明了方法的可行性.     

一类正则Sturm—Liouville问题特征的渐近分析

考虑[0,π]上一类带一般分离型边界条件的正则Sturm—Liouville问题特征的渐近表示,利用Frechet导数,对特征值进行精细的分析,清楚地给出了方程系数q（x）及边界条件中常数cot α,col β对特征值的影响．使结论更具一般化．