这本文集，收集了作者从70年代到现在有关此方面的研究成果和学术论文。其中包括叶轮机械内部流动及叶片设计、柴油机热力气动循环、薄壁构件及壳体理论方法、轴承润滑、核反应堆物理及核电站、重型机械等技术课题中提出的数学问题。反应了作者研究问题的过程是：建立数学模型，探讨数学方法和进行数学分析，最后到研制相关软件。

本书内容涉及叶轮机械内部流动、涡轮增压、柴油发动机热力气动循环、薄壁构造和壳体理论、轴承润滑、核反应堆和核电站运行、Navier—Stokes方程理论和建立在近似惯性流形基础上的算法和维数分裂算法、非线性问题分歧理论和算法等等，这些问题与工程问题有紧密联系，可以为从事相关技术问题研究的读者或在校的研究生提供参考。

A．叶轮机械、柴油发动机、壳体、轴承润滑和地球物理流动

 A Geometrical Design Method for Blade’S Surface Shape and General

 Minimal Surface

 Optimal Shape Design for Blade’S Surface of an Impeller Via the Navier-

 Stokes Equations

 A Dimension Split Method for the 3-D Compressible Navier-Stokes

 Equations in Turbomachine

 Mathematical Aspect of Optimal Control Finite Element Method for

 Navier-Stokes Problems 

 Mathematical Aspect of the Stream—Function Equations of Compressible

 Turbomachinery Flows and Their Finite Element Approximations

 Using Optimal Control

 柴油发动机排气压力波计算

 An Asymptotic Analysis Method for the Linearly Shell Theory

 近代梁工程有限元分析

 On the Uniqueness of the Unbounded Classical Soultion of the

 Evolution System Describing Geophysical Flow within the

 Earth and Its Associated Systems

 On Existence，Uniqueness and L’-Exponential Starbility for Stationary

 Solutions to the M HD Equations in Three-Dimensional Domains 

B．近似惯性流形和Naviev-Stokes方法的惯性算法

 A New Approximate Inertial Manifold and Associated Algorithm

 An AIM and One——Step Newton Method for the Navier——Stokes Equations

 Fourier Nonlinear Galerkin Method for Navier——Stokes Equations 

 时滞惯性流形及近似时滞惯性流形族

 N—S方程一般近似惯性流形构造和逼近

 N0nlinear Galerkin Method for Navier—Stokes Equations with Stream Form

 加罚N—S方程的有限元非线性Galerkin方法

 A Small Eddy Correction Method for Nonlinear Dissipative Evolutionary

 Equations

 Asymptotic Behavior and Time Discretization Analysis for the Non—Stationary

 Navier—Stokes Problem

 Convergence and Stability of Finite Element Nonlinear Galerkin Method

 for the Navier—Stokes Equations

 Uniform Attractors of Non—Autonomous Dissipative Semilinear

 Wave Equations

 无界区域上非自治Navier—Stokes方程的一致吸引子及其维数估计

 非光滑区域上非自治Navier—Stokes方程非齐边界问题的吸引子

 The Stability of Navier—Stokes Equations and the Estimation of Its

 Attractor Dimension 

C．外部问题的边界积分方程和有限元耦合方法

 The Coupling of Boundary Integral and Finite Element Methods for the

 Navier-Stokes Equations in an Exterior Domain

 Stokes Coupling Method for the Exterior Flow Part III：Regularity

 Coupling Method for the Exterior Stationary Navier—Stokes Equations

 Oseen Coupling Method for the Exterior Flow PartⅡ：Well—Posedness

 Analysis

 Oseen Coupling Method for the Exterior Flow Part I：Oseen Coupling

 Approximation

D．非线性方程分歧问题的算法

 Taylor Expansion Algorithm for the Branching Solution of the Navier

 Stokes Equations

 Global Bifurcation and Long Time Behavior of The Volterra—Lotka

 Ecological Model

 Existence and Nonexistence of Global Solutions for the Equation of

 Dislocation of Crystals

 TB点计算的一个分裂迭代方法

 A Splitting Iteration Method for a Simple Corank-2 Bifurcation Problem

 Bifurcation Solution Branches and Their Numerical Approximations of a

 Semi—Linear Elliptic Problem with two Parameters 

 On the Solitary Wave Solutions of the CQNLS

 On Positive Solutions．of the Lotka—Volterra Cooperating Models with

 Diffusion 

 Navier—Stokes方程的非奇异解分支的谱Galerkin逼近

 求解Navier—Stokes方程的非退化转向点的扩充系统的一步牛顿迭代法