具有转向点的二阶非线性问题的奇摄动

具有转向点的二阶非线性问题的奇摄动吴钦宽（芜湖联合大学）１引言关于具有转向点的奇摄动边值问题，人们对线性边界条件的问题都已有不少研究，然而对非线性边界条件的问题的研究成果还不多见。本文考虑如下形式的非线性边值问题。其中。＞０是小参数．ｘ—０是转向点．...     

一类二阶非线性常微分方程非线性边界条件的两点边值问题

本文讨论了一类二阶非线性常微分方程之具有线性边界条件的和具有非线性边界条件的两点边值问题解的存在性.     

抛物问题的边界条件均匀化

椭圆型问题边界条件均匀化的一系列结果已在[1]中得到。本文参照[1]中的方法,对抛物问题的几种边界条件均匀化进行了计论,并得到了与[1]类似的结果。     

对波动方程初边值问题边界条件齐次化函数的一个注解

基于传统的齐次化边界条件方法,采用傅里叶级数法讨论了波动方程初边值问题第一类非齐次边界条件齐次化函数问题,分析表明:对同一定解问题,在不同齐次化函数下的解在适定意义下是等价的.     

一类二阶奇摄动边值问题的激波解

考虑了一个二阶奇摄动非线性边值问题,利用匹配展开法研究了该问题的激波解,讨论了该问题的激波位置与边界条件的关系.     

非局部初值问题解的存在性定理

近来非局部问题的研究日见增多,但涉及带非线性边界条件的初值问题文献 较少.本文目的在于证明一个半线性方程的齐次边值问题和一个非线性边界条件问题 解的存在性.主要使用半群,分数次幂函数空间,广义Poincare算子等工具.     

非线性三阶常微分方程的非线性三点边值问题解的存在性

基于上下解方法,在一定条件下,得到了一类带有非线性混合边界条件的三阶常微分方程的非线性三点边值问题解的存在性,作为上述存在性结果的应用,在推论中给出了一类三阶非线性微分方程三点边值问题解的存在性.     

三阶常微分方程的两点边值问题

本文由二阶常微边值问题的解出发，给出三阶非线性常微分方程两点线性及非线性边界条件下边值问题解的存在性判居。     

非线性四阶常微分方程三点边值问题解的存在性

本文利用文献[1]、[2]的方法,讨论了非线性四阶常微分方程满足如下条件的三点边值问题解的存在性。对于非线性四阶常微子方程的边值问题,到目前已经有了一系列的研究。而本文所讨论的方程(*),具非线性边界条件(**)的边值问题解的存在性,则是上述工作未曾涉及的。本文主要定理的推论,方程(*)之具如下形式的边界条件的边值问题解的存在性,以前的工作也未涉及。     

圆薄板非对称大变形弯曲问题

本文首先导出圆薄板非轴对称大变形问题的位移基本方程及边界条件.利用变换和摄动法将非线性位移方程线性化,得到了近似边值问题.作为算例,文中研究了圆薄板在较复杂载荷作用下的非线性弯曲问题.     

振荡Robin混合边值齐次化问题

该文研究了振荡Robin混合边值齐次化问题解的收敛率.该工作的困难之处在于Robin边值上出现的振荡因子以及边界交叉项的处理.该文利用对偶方法巧妙得对振荡积分进行了估计.文中建立了解的H1和L2收敛率,所得结果明显地依赖于维数.该文可以视为将对偶方法和光滑算子,延拓到处理振荡Robin混合边值问题的情形.     

Boundary value driven approach to computational homogenization

A novel approach to computational homogenization methods for the analysis of heterogeneous structures with large length scale differences between their micro- and macroscale is presented. The boundary value driven approach to homogenization (BVDH) is efficient and reliable compared to existing multi-scale frameworks and the limit cases of homogenization, respectively. Furthermore, the proposed approach is applicable to multi-physical problems such as thermomechanical analysis. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A posteriori error majorants of the modeling errors for elliptic homogenization problems

In this paper, we derive new two-sided a posteriori estimates of the modeling errors for linear elliptic boundary value problems with periodic coefficients solved by homogenization. Our approach is based on the concept of functional a posteriori error estimation. The estimates are obtained for the energy norm and use solely the global flux of the non-oscillatory solution of the homogenized model and solution of a boundary value problem on the cell of periodicity.     

复合材料拟周期结构的均匀化方法

1．预备知识和问题的提出文山讨论了复合材料周期结构的数学问题,即复合材料弹性体的物理参数,几何参数具有某种周期拓扑结构的问题．但在实际问题中,有时还会遇到这些情形,由于受湿热环境和结构设计等因素的影响,弹性体不具有整体周期性,而是具有局部周期性,这就是本文要研究的拟周期性．数学上,这些问题可以表述为下列边值问题：其中fiCR”是有界区域,具有LIPschitz连续边界,A‘巾,旬,＜二。‘x,八,k＝l,…,n．是nXn阶矩阵,满足下列的A一条件．J．L．Lions（见文门）等曾对拟周期的二阶椭圆型边值问题进行了讨论,…     

Estimates of modeling errors for linear elliptic problems

We derive new estimates of modeling errors for linear elliptic boundary value problems with periodic coefficients solved by homogenization method. Our approach is based on the concept of functional a posteriori error estimation. The estimates are obtained for the energy norm and use solely the global flux of the non-oscillatory solution of the homogenized model and solution of a boundary value problem on the cell of periodicity. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On homogenization of solutions of the poisson equation in a perforated domain with different types of boundary conditions on different cavities

In this paper we consider boundary value problems in perforated domains with periodic structures and cavities of different scales, with the Neumann condition on some of them and mixed boundary conditions on others. We take a case when cavities with mixed boundary conditions have so called critical size (see [1]) and cavities with the Neumann conditions have the scale of the cell. In the same way other cases can be studied, when we have the Neumann and the Dirichlet boundary conditions or the Dirichlet condition and the mixed boundary condition on the boundary of cavities.There is a large literature where homogenization problems in perforated domains were studied [2];-[7];     

Low-cost control problems on perforated and non-perforated domains

We study the homogenization of a class of optimal control problems whose state equations are given by second order elliptic boundary value problems with oscillating coefficients posed on perforated and non-perforated domains. We attempt to describe the limit problem when the cost of the control is also of the same order as that describing the oscillations of the coefficients. We study the situations where the control and the state are both defined over the entire domain or when both are defined on the boundary.     

Some homogenization problems for the system of elasticity with nonlinear boundary conditions in perforated domains

The system of linear elasticity is considered in a perforated domain with an ε-periodic structure. External forces nonlinearly depending on the displacements are applied to the surface of the cavities (or channels), while the body is fixed along the outer portion of its boundary. We investigate the asymptotic behavior of solutions to such boundary value problems asε→0 and construct the limit problem, according to the external surface forces and their dependence on the parameter ε. In some cases, this dependence results in the homogenized problem having the form of a variational inequality over a certain closed convex cone in a Sobolev space. This cone is described in terms of the functions involved in the nonlinear boundary conditions on the perforated boundary. A homogenization theorem is also proved for some unilateral problems with boundary conditions of Signorini type for the system of elasticity in a perforated domain. We discuss some cases when the homogenized tensor may depend on the functions specifying the boundary conditions.     

Homogenization of Boundary Value Problems in Plane Domains with Frequently Alternating Type of Nonlinear Boundary Conditions: Critical Case

In the present paper we consider a boundary homogenization problem for the Poisson’s equation in a bounded domain and with a part of the boundary conditions of highly oscillating type (alternating between homogeneous Neumman condition and a nonlinear Robin type condition involving a small parameter). Our main goal in this paper is to investigate the asymptotic behavior as ε → 0 of the solution to such a problem in the case when the length of the boundary part, on which the Robin condition is specified, and the coefficient, contained in this condition, take so-called critical values. We show that in this case the character of the nonlinearity changes in the limit problem. The boundary homogenization problems were investigate for example in [1, 2, 4]. For the first time the effect of the nonlinearity character change via homogenization was noted for the first time in [5]. In that paper an effective model was constructed for the boundary value problem for the Poisson’s equation in the bounded domain that is perforated by the balls of critical radius, when the space dimension equals to 3. In the last decade a lot of works appeared, e.g., [6–10], in which this effect was studied for different geometries of perforated domains and for different differential operators. We note that in [6–10] only perforations by balls were considered. In papers [11, 12] the case of domains perforated by an arbitrary shape sets in the critical case was studied.     

HOMOGENIZATION OF SOME LINEAR AND SEMILINEAR SCHRDINGER EQUATIONS WITHREAL POTENTIAL

1 IntroductionIn this paPer, we collsider the initial and boundaxy value probIem of linear and sentilillearScl1r5dinger equation as fOllows:l ie(x):5:i".,'<">"'>.'<",,'>,"=' 1:!\:?0t:)t>, (l1)wllere E > 0, fl C RN is a bounded open dolllain and T is an ar…