拟线性抛物型积分微分方程的一个新最低阶混合元格式

对一类拟线性抛物型积分微分方程构造了一个新的最低阶三角形协调混合元格式,并直接利用单元插值的性质,给出了相应的收敛性分析和H~1-模及L~2-模意义下的最优误差估计.     

一类二阶常微分方程奇异边值问题多重解的至少个数

本文利用变分原理和Z2不变群指标研究了二阶常微分方程边值问题的多重解．得出了这类解个数的下界估计     

变分方法对具有Stark势非线性Schr(o)dinger方程的应用

本文讨论一类具有Stark势的非线性Schr(o)dinger方程,通过构造一个交叉强制变分问题和发展流的所谓不变流形,得到一个解爆破和整体存在的最佳准则.同时证明了驻波的不稳定性.     

AN EXTRAGRADIENT METHOD FOR RELAXED COCOERCIVE VARIATIONAL INEQUALITY AND EQUILIBRIUM PROBLEMS

The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.     

The Study of KKM Theorems With Applications to Vector Equilibrium Problems and Implict Vector Variational Inequalities Problems

In this paper, we establish some equivalence relations between coincidence theorems and KKM-type theorems. We also obtain some new coincidence theorems and fixed point theorems. Applying the KKM-type theorems we obtain the existence theorems of generalized vector equilibrium problems. From these results, some existence theorems of generalized vector implicit variational inequality problems are established in this paper.     

Coordinate Transformation Method for the Extremization of Multiple Integrals

In this paper, we generalize a coordinate transformation method, due to Leitmann (Ref. 1), for free problems in the calculus of variations to analogous problems with multiple integrals.     

Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities

We consider a useful modification of the inexact implicit method with a variable parameter in Wang et al. J Optim Theory 111: 431–443 (2001) for generalized mixed monotone variational inequalities. One of the contributions of the proposed method in this paper is that the restrictions imposed on the variable parameter are weaker than the ones in Wang et al. J Optim Theory 111: 431–443 (2001). Another contribution is that we establish a sufficient and necessary condition for the convergence of the proposed method to a solution of the general mixed monotone variational inequality.     

On variational approximations in quantum molecular dynamics

The Dirac-Frenkel-McLachlan variational principle is the basic tool for obtaining computationally accessible approximations in quantum molecular dynamics. It determines equations of motion for an approximate time-dependent wave function on an approximation manifold of reduced dimension. This paper gives a near-optimality result for variational approximations. It bounds the error in terms of the distance of the exact wave function to the approximation manifold and identifies the parameters that control the deviation of the variational approximation from the best approximation on the manifold.

     

Quasilinear first-order PDEs with hysteresis

This paper deals with the Cauchy problem for a quasilinear first-order equation that includes a possibly discontinuous hysteresis operatorF:

     

Analysis of flow in the plate‐spiral of a reaction turbine using a streamline upwind Petrov–Galerkin method

The prediction of the flow field in a novel spiral casing has been accomplished. Hydraulic turbine manufacturers are considering the potential of using a special type of spiral casing because of the easier manufacturing process involved in its fabrication. These special spiral casings are known as plate‐spirals. Numerical simulation of complex three‐dimensional flow through such spiral casings has been accomplished using a finite element method (FEM). An explicit Eulerian velocity correction scheme has been deployed to solve the Reynolds‐average Navier–Stokes equations. The simulation has been performed to describe the flow in high Reynolds number (10⁶) regimes. For spatial discretization, a streamline upwind Petrov–Galerkin (SUPG) technique has been used. The velocity field and the pressure distribution inside the spiral casing reveal meaningful results. Copyright © 2000 John Wiley & Sons, Ltd.