该方程组涵盖了变分问题的各种欧拉方程。
The complete Euler equation set contains all kinds of Euler equations of the variational problems.
然后根据这个估计式，将问题化成求解一个条件变分问题。
Using this estimate, it may be simplified to solve a problem of the conditional variation.
一般情况下，是把变分问题化成微分方程的边值问题来处理。
In the ordinary circumstances, it turns the variation question into the boundary value question of the differential equation problem to process.
在此意义下，把变分问题归结到边值问题，反而将问题复杂化了。
Under this significance, it sums up the variation question to the boundary value question, instead complicated question.
通常，源于大偏差方法的小概率事件的概率可以作为一个变分问题的解。
Usually the probability of rare event derived from large deviation method can be expressed as a solution of variational problem.
有限元法实质上是变分问题的一种数值解法，是物理问题的通用计算方法。
Essentially, the finite element method is a numerical technique for the variational problems, which is a general approach to physical problems.
文中引入了一类广义不变凸函数，对一类变分问题给出了最优解的充分性条件以及对偶理论。
The generalized invex functions are introduced and the optimality theorems and duality theory are established for a class of variational problems.
采用最小二乘法对弹性接触问题提出了一种新的混合变分形式，对该变分问题解的存在唯一性进行了论证。
A new mixed variational formulation is presented for the elastic contact problem with application of least-square method.
给出了分段线性函数族的定义和有关的运算性质，利用这些性质得到直接求解变分问题的一种新的数值方法。
The definition of the Segmental Linear Functions and some operational properties are given. By means of the properties, a new numerical method for direct solving variational problems is obtained.
通过对一类相当复杂的变分方程问题的研究并利用其有关结论，我们证明了新模型最佳控制的存在性并刻划出其结构。
From studying some kind of quite complex variational equation problems and applying the conclusion, we prove that the optimal control of new model is existent and characterize its structure.
这种新的变分原理能反映动力学初值-边值问题的全部特征。
The new variational principles can fully characterize the initial-boundary-value problem of this dynamics.
然而，混凝土的徐变及其对桥梁结构性能影响的预计和控制，是十分复杂又难以获得精确答案的问题。
However, creep of concrete and its influence on bridge structures are hard to predict and control. The calculation is very complicated and the results are not accurate.
高速网络中变比特率业务的流量控制和带宽分配问题另一个十分重要的研究方向。
Flow control and bandwidth allocation for VBR traffic on high speed network are also very important research directions.
在耦合热弹性问题变分原理的基础上，导出非定常温度场热弹性平面问题的有限元法基本方程。
The fundamental equations in finite element method for unsteady temperature field elastic plane problem are derived on the bases of variational principle of coupled thermoelastic problems.
作为哈密顿力学逆问题，从弹性力学基本方程推导出弹性力学中一个新的哈密顿系统及其变分原理。
As an inverse problem of Hamiltonian mechanics, a new Hamiltonian system in elasticity and its variational principle are derived from the basic equations of elasticity.
变分原理的建立将有利于压电材料圆柱壳静力学和动力学问题的有限元方法或半解析法的推导。
The establishment of variation-principle is of benefit to deriving the finite element method or semi-analytical solution to the cylindrical shell static-dynamical problems of piezoelectric materials.
然后引入新的步长函数空间，并在这个空间上，采用变分近似法讨论该格式的稳定性问题。
Then the new step function space is introduced and stability problem for the finite difference scheme is discussed by means of variational approximation method.
本文给出了非线性弹性动力学两时端边值问题的某些一般定理及变分原理。
In this paper, some general theorems and variational principles of the boundary value problem for two time instants in nonlinear elastodynamics are developed.
本文提出了求解摄动问题的一种新方法——变分迭代算法。
In this paper, a novel method called the variational iteration method is proposed to solve perturbation problems.
然后引入新的函数空间，并在这个空间上，采用变分近似法讨论了该格式的稳定性问题。
Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space.
研究了变分学中的逆问题。
对于变分同化中经常遇到的多极值问题，一般的优化算法无法解决。
The ordinary optimization algorithm can not solve the multi-extreme value problem in data assimilation, so an improvement to steepest descent algorithm is proposed to solve the problem.
提出了一个包括界面条件及间断面条件在内的混合边值问题的广义变分原理，建立了极限载荷乘子的变分解析公式。
A generalized variational principle involving conditions of the rigid-plastic interface and the discontinuous surface of a velocity field has been put forward for the mixed-boundary value problem.
时变参数的估计问题，对于动态系统的控制是十分重要的。
Time varying parameter estimation is very important to the control of dynamic system.
变分复形是用来研究拉氏系统的理论工具，利用一个正合的变分复形可以解决很多变分法方面的问题。
A variational complex is a theoretical tool for the rigorous study of Lagrangian systems. Using an exact variational complex can solve many problems about the variational calculus.
本文提出一种用分区变分原理和样条函数相结合的有限元方法，解决组合型旋转壳受力分析问题。
A finite element method using subregion variational principle and spline function in this paper is presented to solve the problem of combined shell of revolution.
再得到与之对应的各类变分原理，界限定理，第二阶段问题的边界积分方程。
Then correspondently, we obtain the specific variational principles, bounded theorems, and boundary integral equations of the second stage problems.
从卷积型变分原理的泛函出发，通过分析泛函中的各项，推导出求解动力响应问题的时-空有限元法，并将其应用于梁的动力问题中。
Based on Gurtin type variational principle a finite element method for initial value problems is presented by functional analysis. It is used for problems of beams dynamics.
从卷积型变分原理的泛函出发，通过分析泛函中的各项，推导出求解动力响应问题的时-空有限元法，并将其应用于梁的动力问题中。
Based on Gurtin type variational principle a finite element method for initial value problems is presented by functional analysis. It is used for problems of beams dynamics.
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