扩散引起的爆破问题

众所周知,在某些条件下常微分方程的解有限时刻爆破,与之相应的带齐次Ｄｉｒｉｃｈｌｅｔ边界条件的反应扩散方程的解整体存在也就是说,扩散阻止了解有限时刻爆破一个自然的问题;常微分方程的解是否整体存在,而与之相应的带齐次Ｄｉｒｉｃｈｌｅｔ边界条件的反应扩散方程的解是否有限时刻爆破？即扩散能否引起解有限时刻爆破？本文将通过一个简单的例子给此问题一个确切的答案     

光滑区域上Hermite插补多项式同时逼近函数及其导数

设Ｄ是复平面上的Ｊｏｒｄａｎ区域，｛ｚｋ｝ｎ－１ｏ是Ｄ上的Ｆｅｊｅｒ点．考虑用Ｈｅｒｍｉｔｅ插值多项式逼近Ｄ内的函数及其导数，在某些边界条件下得出了一致逼近与平均逼近的阶．     

拟线性椭圆型方程组正解的存在性和唯一性

本文讨论了某些带Ｄｉｒｉｃｈｌｅｔ边界条件的非线性椭圆型方程组正解的存在性和唯一性，给出了正解 存在和唯一的充要条件，     

一类阻尼边界条件下的逆散射问题

１．引言 考虑声波在均匀非吸收介质中的传播,该声波被一个无限长的柱体所散射．在声波线性化理论中,众所周知,时间调和声波的振幅ｕ（ｘ）满足 Ｈｅｌｍｈｏｌｔｚ方程其中波数ｋ＝＞０时间调和声波的散射可以用方程（１．１）的适当的边界条件（例如Ｄｉｒｃｈｌｅｔ条件或Ｎｅｕｍａｎｎ条件）来描述．特别,ｕ｜Ｄ＝０对应于软边界（ｓｏｕｎｄ－ｓｏｆｔ）散射,而Ｄ＝ ０则是所谓的硬边界（ｓｏｕｎｄ－ｈａｒｄ）散射·这里 γ表示边界 Ｄ的外法向． 除了上述两类条件外,还有一类更能描述现实物理现象的阻尼边界条件,即物理上,…     

抛物型初边值问题的自然积分方程及其数值解法

１．引言数值求解无界区域的偏微分方程,自然的处理方式是削去区域的无界部分,即引入一条适当的人工边界ｒ。,将原问题的求解限制在一个适当的有界区域Ｄ内,这样必须在人工边界上引入适当边界的条件．于是很自然地导致这样一个问题：'是否存在一个人工边界条件,使得在这边界条件下,原问题在区域Ｄ内所求得的数值解与原无界区域的解在Ｄ上的限制是完全一致的？"这里我们的着眼点是寻求与原无界区域问题等价的数学形式,以便于数值求解．因为边界元方法可以将区域内的问题转化到区域的边界上去处理,经典的边界元方法常被应用．七十年代…     

一类广义单种群模型的正确及其稳定性

本文讨论了在齐次Ｄｉｒｉｃｈｌｅｔ边界条件下具有扩散现象的一类广义单种群模型的正定态解。给出了使得严格正解存在的λ的取值范围，并且讨论了当λ充分大时正解的稳定性。     

关于耗散波动方程精确能控性的奇异极限的一个注记

本文在比文献［１］更一般的几何控制条件下，分析了具齐次Ｄｉｒｉｃｈｌｅｔ边界条件的耗散波动方程精确能控性的奇异摄动问题．结论是由这类波动方程的精确能控性可得到热传导方程的精确零能控性．     

一类椭圆型方程Numann 问题无穷多解的存在性

本文给出了Ｒ~Ｎ（Ｎ≥３）上有光滑边界的边界区域Ω上带临界增长的拟线性椭圆型方程在边界条件Ｆｉ（ｘ，ｕ，Ｄｕ）ｃｏｓ（ｎ，ｘｉ）＝ ０下无穷多解的存在性．     

关于Schrodinger算子的任意相邻两特征值之差的上界估计

设Ω是Ｒ＾ｎ中有界光滑区域，用γ记Ω上Ｓｃｈｒｏｄｉｎｇｅｒ算子的具Ｄｉｒｉｃｈｅｔ边界条件的特征值问题的第ｉ个特征值。本文利用极大极小原理研究任意相邻两特征值之差λｋ＋１－λＫ的上界，推广了Ｐａｙｎｅ和Ｓ．Ｔ．Ｙａｕ等人的有关结果。     

耦合Sine-Gordon方程组的渐近行为

本文考虑带Ｄｉｒｉｃｈｌｅｔ边界条件的耦合Ｓｉｎｅ－Ｇｏｒｄｏｎ方程组的渐近行为．证明了整体吸引子的存在性,并给出了整体吸引子的Ｈａｕｓｄｏｏｆ维数的上界估计．本文的估计与文［９］的结果相比有本质上的改进．在参数满足一定条件下,证明了整体吸引子恰好是系统的唯一平衡点     

On viscous incompressible flows of nonsymmetric fluids with mixed boundary conditions

In this paper we are concerned with the initial boundary value problem for the micropolar fluid system in nonsmooth domains with mixed boundary conditions. The considered boundary conditions are of two types: Navier’s slip conditions on solid surfaces and Neumann-type boundary conditions on free surfaces. The Dirichlet boundary condition for the microrotation of the fluid is commonly used in practice. However, the well-posedness of problems with different types of boundary conditions for microrotation are completely unexplored. The present paper is devoted to the proof of the existence, regularity and uniqueness of the solution in distribution spaces.     

Generalized boundary conditions on representative volume elements and their use in determining the effective material properties

We discuss generalized boundary conditions for representative volume elements (RVE), which include the classical boundary conditions as special cases. From the generalization, stochastic boundary conditions are derived. These allows to adjust the the stiffness of the boundary conditions smoothly between the extremal cases of homogeneous strain and homogeneous stress boundary conditions. We found that it needs to be distinguished between the resistance of the boundary conditions against homogeneous and inhomogeneous RVE deformation. The stochastic BC can combine the moderate stiffness of the well known periodic boundary conditions with the high resistance against localization of the homogeneous strain boundary conditions. (© 2013 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];     

Multidimensional Kagiwada-Kalaba method of invariant imbedding with general linear implicit boundary conditions

The Kagiwada-Kalaba method of invariant imbedding for multidimensional systems is first derived for the split linear implicit boundary conditions. The justification for the Kagiwada-Kalaba procedure is explained in terms of the special nature of the split linear implicit boundary conditions. Extension of the Kagiwada-Kalaba method from the split linear implicit boundary conditions to general linear implicit boundary conditions is described.     

常型Sturm-Liouville问题的左定边值条件

本文刻画了常型Sturm-Liouville问题的左定边值条件．通过Sturm-Liouville微分算式的系数、区间端点以及边值条件给出了其左定性的充要条件．应用自伴边值条件分类,确切地给出了所有可能的左定边值条件．     

Canonical forms for boundary conditions of self-adjoint differential operators

Canonical forms of boundary conditions are important in the study of the eigenvalues of boundary conditions and their numerical computations. The known canonical forms for self-adjoint differential operators, with eigenvalue parameter dependent boundary conditions, are limited to 4-th order differential operators. We derive canonical forms for self-adjoint $2n$-th order differential operators with eigenvalue parameter dependent boundary conditions. We compare the 4-th order canonical forms to the canonical forms derived in this article.     

Matrix representations of Sturm‐Liouville problems with coupled eigenparameter‐dependent boundary conditions and transmission conditions

We study matrix representations of Sturm‐Liouville problems with coupled eigenparameter‐dependent boundary conditions and transmission conditions. Meanwhile, given any matrix eigenvalue problem with coupled eigenparameter‐dependent boundary conditions and transmission conditions, we construct a class of Sturm‐Liouville problems with given boundary conditions and transmission conditions such that they have the same eigenvalues.     

Polarization of vacuum with nontrivial boundary conditions

In the framework of the zeta-regularization approach, we consider the polarization of the scalar field vacuum with nontrivial boundary conditions originating from electrodynamics in the presence of a conducting infinitely thin boundary layer. Boundary conditions of the first type correspond to the case where the field is continuous on the boundary while its derivative has a jump proportional to the boundary value of the field. Boundary conditions of the second type correspond to the case where the field derivative is continuous on the boundary but the field itself has a jump proportional to the field derivative on the boundary. We explicitly obtain the zeta function of the scalar field Laplace operator with the above boundary conditions and calculate all the heat kernel coefficients. We obtain an expression for the energy of the scalar field vacuum fluctuations.     

Long-time behaviour of absorbing boundary conditions

A new class of computational far-field boundary conditions for hyperbolic partial differential equations was recently introduced by the authors. These boundary conditions combine properties of absorbing conditions for transient solutions and properties of far-field conditions for steady states. This paper analyses the properties of the wave equation coupled with these new boundary conditions: well-posedness, dissipativity and convergence in time.     

一类拟线性系统的Lyapunov不等式

本文研究了一类拟线性系统，引入了反周期边值条件，基于反周期边值条件和数学分析的技巧，建立了新的Lyapunov不等式．