具有快慢层的非光滑奇异摄动问题的空间对照结构

该文研究了具有快慢层的非光滑奇异摄动问题的空间对照结构.利用边界层函数法构造了该问题的形式渐近解,并运用"缝接法"证明了问题光滑解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.     

一类拟线性奇异摄动方程组的空间对照结构

本文研究带慢变量的右边不连续的拟线性奇异摄动方程组的空间对照结构.利用边界层函数法构造了该方程组的形式渐近解,并运用"缝接法"证明问题解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.     

变系数MDDEs系统的数值稳定性

１．引言考虑下列变系数ＭＤＤＥｓ系统其中　　是复Ｎ级连续矩阵函数,是光滑时滞函数, 是光滑初始函数．下文中,我们恒设（１．１）有唯一光滑解ｙ（ｔ）．对于系统（１．１）的一些子系统,如单滞量系统、多滞量常系数系统,其理论解与数值解的渐近稳定性已被广泛研究（参见［１－４］,特别是在研究数值解的渐近稳定性时, Ｐｍ－、 ＧＰｍ－稳定性概念被提出,其实质是指数值解｛ｙｎ｝以 ０为其吸引点, Ｌ．Ｔｏｒｅｌｌｉ［５,６］则针对单滞量标量线性系统及一般非线性单滞量系统分别提出了另一类稳定性概念,即 ＧＰＮ－稳定与…     

一类具有转点的右端不连续奇摄动边值问题

研究了一类具有转点的右端不连续二阶半线性奇摄动边值问题解的渐近性.首先,在间断处将原问题分为左右两个问题,通过修正左问题退化问题的正则化方程,提高了左问题渐近解的精度,并利用Nagumo定理证明了左问题光滑解的存在性.其次,证明了右问题具有空间对照结构的解,并通过在间断点的光滑缝接,得到了原问题的渐近解.最后,通过一个算例验证了结果的正确性.     

具有不连续源的奇摄动边值问题

本文研究了具有不连续源的奇摄动边值问题.利用边界层函数法和缝接法,得到了整个区间上原问题解的一致有效的渐近表达式.     

一维可压缩Navier-Stokes-Korteweg方程组的大初值整体光滑解

本文研究了当粘性系数和毛细系数是密度函数的一般光滑函数时,一维等温的可压缩NavierStokes-Korteweg方程的Cauchy问题.利用基本能量方法和Kanel的技巧,得到了大初值、非真空光滑解的整体存在性与时间渐近行为.本文结果推广了已有文献中的结论.     

具有内部层的奇摄动微分差分方程的渐近解

该文针对一类非线性奇摄动微分差分方程边值问题,用边界层函数法构造了一致有效的渐近解.由于偏差效因,边界层函数的确定困难很多.作者用"缝接法"不但证明了光滑解的存在性,而且给出了余项估计.     

非线性扰动Klein-Gordon方程初值问题的渐近理论

在二维空间中研究一类非线性扰动Klein-Gordon方程初值问题解的渐近理论. 首先利用压缩映象原理,结合一些先验估计式及Bessel函数的收敛性,根据Klein-Gordon方程初值问题的等价积分方程,在二次连续可微空间中得到了初值问题解的适定性;其次,利用扰动方法构造了初值问题的形式近似解,并得到了该形式近似解的渐近合理性;最后给出了所得渐近理论的一个应用,用渐近近似定理分析了一个具体的非线性Klein-Gordon方程初值问题解的渐近近似程度．     

具有积分边界条件的二阶半线性奇摄动方程脉冲状对照结构(英文)

本文讨论了带有积分边界条件的二阶半线性奇摄动方程的脉冲状对照结构.借助于边界函数法,在一定条件下,构造了该问题的形式渐近解.利用缝接法证明了该问题解的存在性和形式渐近解的一致有效性.     

一类拟线性奇摄动流体模型的渐近分析

对一类拟线性流体模型进行研究,借助Linard变换将所研究问题转化为可以用边界函数法处理的问题,进而用边界函数法对该方程组进行分析,构造其(n+1)阶形式渐近解,并证明解的存在唯一性和形式渐近解的一致有效性.     

NEUMANN BOUNDARY VALUE PROBLEM FOR THE LANDAU-LIFSHITZ EQUATION

In this paper, we prove that there exists a unique global smooth solution for the homogeneous Neumann boundary value problem of the Landau-Lifschitz equation if the initial function is smooth.     

多圆柱域上带间断系数的边值问题

本文研究多个复变数解析函数在多圆柱区域上带间断系数的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ边值问题。文中给出了这个问题适定的变态提法，首先证明了相应变态问题解的存在唯一性。然后给出原边值问题可解的充要条件及解的积分表达式。     

一阶非线性椭圆型复方程的间断Riemam边值问题

§1 问题的提法 本文讨论一阶非线性一致椭圆型复方程 的间断非线性Riemann边值问题。以E表示复平面,D~ 表示有界N 1连通区域,其边界由     

Error estimates for a discontinuous Galerkin method for elliptic problems

In this paper, we consider an elliptic problem with the homogeneous Dirichlet boundary condition and introduce discontinuous Galerkin approximations of the problem. Optimal error estimates of discontinuous Galerkin approximations are obtained.     

STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS

1IntroductionIt is well-known that the Sturmian Theory is an important aid in solving many problemsin mathematical physics.Therefore this theory is one of the most actual and extensivelydeveloped field in spectral analysis of boundary-value problems of St…     

Resolvent Operator and Self-Adjointness of Sturm–Liouville Operators with a Finite Number of Transmission Conditions

In this paper, we consider a Sturm–Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at a finite number of interior points. We introduce a Hilbert space formulation such that the problem under consideration can be interpreted as an eigenvalue problem for a suitable self-adjoint linear operator. We construct Green function of the problem and resolvent operator. We establish the self-adjointness of the discontinuous Sturm–Liouville operator.     

Esistenza ed unicita’ delle soluzioni di un problema misto per un sistema iperbolico simmetrico con coefficienti discontinui

In this paper we give existence and uniqueness theorems for weak solutions of a mixed initial and boundary value problem with conservative boundary conditions relating to a particular symmetric hyperbolic linear system with discontinuous coefficients. The unicity is proved also for a mixed non linear problem.     

An elliptic boundary problem in a half–space

The spectral theory for general non–selfadjoint elliptic boundary problems involving a discontinuous weight function has been well developed under certain restrictions concerning the weight function. In the course of extending the results so far established to a more general weight function, there arises the problem of establishing, in an L_p Sobolev space setting, the existence of and a priori estimates for solutions for a boundary problem for the half–space ?ⁿ₊ involving a weight function which vanishes at the boundary x_n = 0. In this paper we resolve this problem.     

SINGULARLY PERTURBED SEMI-LINEAR BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS FUNCTION

A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article.Using the boundary layer function method,the asymptotic solution of such a p...     

Some new analysis results for a class of interface problems

Interface problems modeled by differential equations have many applications in mathematical biology, fluid mechanics, material sciences, and many other areas. Typically, interface problems are characterized by discontinuities in the coefficients and/or the Dirac delta function singularities in the source term. Because of these irregularities, solutions to the differential equations are not smooth or discontinuous. In this paper, some new results on the jump conditions of the solution across the interface are derived using the distribution theory and the theory of weak solutions. Some theoretical results on the boundary singularity in which the singular delta function is at the boundary are obtained. Finally, the proof of the convergency of the immersed boundary (IB) method is presented. The IB method is shown to be first‐order convergent in L ^∞ norm. Copyright © 2013 John Wiley & Sons, Ltd.