The Signaling Problem in Nonlinear Hyperbolic Wave Theory

This work is devoted to investigating weakly nonlinear hyperbolic waves arising from the action of small-amplitude, high-frequency boundary disturbances. By directly introducing a nonlinear phase variable corresponding to the leading wavefront and specifying a single-wave-mode boundary disturbance, we are able to construct an asymptotic solution. Furthermore, our result shows that, by properly arranging the relation of small amplitude to high frequency, a systematic procedure can be provided for constructing weakly nonlinear wave solutions with interior shocks and determining the shock initiation position (and time) when there is a local linear degeneracy at the leading wavefront.     

Isoparametric, Finite Element Methods for Nonlinear Dirichlet Problem

In this paper, the author solves the nonlinear Dirichlet problem with nonhomo- genous boundary condition by use of the isoparametric finite element method, and obtains the optimal error estimate.     

TWO-GRID CHARACTERISTIC FINITE VOLUME METHODS FOR NONLINEAR PARABOLIC PROBLEMS＊

In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.     

广义 Eady 模型的非线性稳定性

对于广义 Eady 模型, 分别讨论了密度函数是常数函数与指数函数两种情形, 利用变分原理, 考虑到动量守恒的约束条件, 得到了优化的 Poincaré不等式, 从而得到了新的非线性稳定性定理, 并且得到了在径向长度分别不大于纬向长度的0.84402倍 及 0.86068 倍时(这对于地球的实际情况是成立的), 非线性稳定性判据与线性稳定性判据是一致的.     

广义Eady模型的非线性稳定性

对于广义Eady模型，分别讨论了密度函数是常数函数与指数函数两种情形，利用变分原理，考虑到动量守恒的约束条件，得到了优化的Poincare不等式，从而得到了新的非线性稳定性定理，并且得到了在径向长度分别不大于纬向长度的0．84402倍及0．86068倍时（这对于地球的实际情况是成立的），非线性稳定性判据与线性稳定性判据是一致的．     

非线性常微分方程初值问题的间断有限元

该文用m次间断有限元求解非线性常微分方程初值问题u'=f(x,u),u(0)=u₀,用单元正交投影及正交性质证明了当m≥1时,m次间断有限元在节点x_j的左极限U(x_j-0)有超收敛估计(u-U(x_j-0)=O(h^2m+1),在每个单元内的m+1阶特征点x_ji上有高一阶的超收敛性(u-U)(x_ji)=O(h^m+2).     

不动点定理在奇摄动非线性初值问题的套层解中的应用

Singularperturbationofnonlinearboundaryvalueproblemswhichhavedoubleboundarylayerpropertieswerediscussedbysomeauthorsusingthemethodofdifferentialinequali ties[1 ] -[3 ] .Nonlinearboundaryvalueproblemswhichhavenotdoubleboundarylayerpropertieswerediscussedbysomeauthorsusingthemethodofthefixed_pointtheorem[4] -[6 ] .Inthispa perwewillusethefixed_pointtheoremtodiscussthethirdorderdifferentialequationswhichhavedoubleinitiallayer.Weconsiderthefollowingproblem .ε4y =h(t,y,εy′,ε2 y″,ε) ,t∈ [0 ,T…     

大变形非线性弹性力学的广义变分原理

本文导出了大变形非线性弹性力学的两个具有σ_ij,e_ij,和u_i三类独立变量的广义变分原理,证明了当应力应变关系为约束条件时这两个广义变分原理是等价的.文中对某些特例也作了阐明.     

The Stefan Problem with Nonlinear Convection

In this paper, we consider the time dependent Stefan problem with convection in the fluid phase governed by the Navier-Stokes equation and with adherence of the fluid on the lateral boundaries. The existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation, together with the application of various compactness arguments.     

The Finite Element Method for Nonlinear Elasticity

In this paper we consider the finite element method for nonlinear elasticity in the case when body force is small. The incremental method and the improved incremental method are investigated, their convergence are proved and the error estimates are obtained.     

The Hausdorff Moment Problem under Finite Additivity

We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.     

三角形二次插值系数有限元法解半线性椭圆问题的超收敛性

基于均匀三角形的剖分求解一类二阶半线性椭圆问题,用插值系数有限元方法比经典有限元法更容易实现,与经典二次有限元一样,二次插值系数有限元方法在对称点处也有四阶超收敛精度,数值计算表明这些结论是正确的.     

The Local Stabilizability Problem for Nonlinear Systems

This paper deals with the local smooth stabilizability problemfor nonlinear control systems defined by ordinary differentialequations. Several approaches to this problem are reviewed anddiscussed: in particular, it is shown that certain results canbe improved (at least from a practical point of view) by combiningdifferent approaches.     

非线性散射问题

三维介质中的谐波在遇到障碍物后的散射同题,数学上可表示为Helmholtz方程的边值问题,其中无穷远点满足Sommerfeid散射条件.在非线性介质中,波动方程可表示为utt-c2Au=F(x,u),当F(x,u)满足适当条件时,代入入射波的表达式U(x,t)=e-iwtu(x),即得到在有界区域内散射波满足的方程Au k21u=f(x,u).对非线性介质在小跳跃度和小扰动下散射问题的解的存在性进行讨论,同时对一类非线性函数f(x,u)在大跳跃度情况下给出散射问题解的存在性.     

奇摄动非线性边值问题

本文研究了奇摄动非线性边值问题(?)其中y,f,A,B为n-维向量．在适当的假设下作者利用微分不等式方法证明了存在一个解y(x,ε) ,并得到了它的估计式．     

The Static Theory of Finite Elasticity

A review of the equilibrium theory of finite deformations ofelastic solids and its applications, with special emphasis onapproximate methods of solution of problems.     

论连续体力学非线性场论中有限转动的表现

连续体力学发展中的一个重要基本理论问题就是如何从位移场确定场中每一点的应变与转动。经过近年来的研究与各方面探讨,已经证明S-R分解定理的理论价值,在今后连续体力学发展中将具有重要的作用。本文目的在于澄清变形体有限转动的一些基本概念,促进应用进展。