变分问题

Tangent linear and adjoint method of "on-off " switches are studied in this paper.

本文研究了四维变分资料同化中有关"开关"变量的切向线性化和伴随问题。

The existence theorem of solution of approximate problems is obtained.

我们考虑了一类广义似变分不等式系统的数值解，提出和SGVLIP相关的逼近问题，证明了逼近问题解的存在性。

Two consistent systems for elasticity, the Axiomatic System of Variation and the Formal System of Variation, are suggested in this paper.

他事实上认为变分原理中的变量独立是不证自明的或理所当然的[14]。但是变量独立的问题并没有解决，因为在他的系统中也存在着矛盾。

Accordingly, on the hypothetical condition that the material coefficients are the linear functions of tem perature and according to the theory of functional analysis, the authors use the method of combing the inner product form with convolution bilinear form, which leads to the functional of the quasistatic coupled thermo—viscoelasticity including the boundary and initial c...

因此，著者在物性系数是温度的线性函数的假设条件下，根据泛函分析理论，采用内积式与卷积双线性式相结合的方法，导出了包含所有边界条件，初始条件及热传导方程的拟静态耦合热粘弹性问题的泛函，并证明了与之相应的变分原理。

By using thenatural boundary element method which is set up by professor Feng Kang,the Neu-mann boundary problem of the harmonic equation on the half-upper plane is reducedto the Hadamard type singular integral equation,the integral region of which is un-bound,and then we turn it into corresponding bilinear form.

通过由冯康教授开创的自然边界元方法，将上半平面调和方程的Neumann边值问题归化为Hadamard型强奇异自然边界积分方程，并且此积分方程是无界域上的强奇异自然边界积分方程，然后将它转化为相应的变分形式。

The exact form of exterior boundary value problems for plane potential problem is established with variational principle.

使用变分法确立平面 Laplace外问题的确切形式；在此基础上，为了避免使用无限区域上的 Green公式，通过构造紧支集上的无穷可微函数，获得满足非齐次控制微分方程的特解的重要结果。

But we can prove that the corresponding Eulur\'s function is bounded from below in a proper set S of W_0~(1,p)× W_0~(1,q), and then a minimizer of Eulur\'s function in S gives rise to a solution of the problem.

但是，我们可以证明欧拉泛函在合适的集合S中有下界，因此在该集合中利用变分方法寻找泛函的极小就可以得到原问题的解。

This method is based on the work of reference [1]. By using the Riesz present theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixed point theory, we construct a numerical verification method with high efficiency that through numerical computation generates a bounded, closed, convex set in which the approximate solution is included.

通过Hilbert空间中的Riesz表示定理，首先将变分不等式问题的迭代过程转化为一种不动点形式，再利用Schauder不动点定理构造了一个高效率的数值证明过程，即通过数值计算产生一个包含近似解的有界闭凸子集。

The brachistochrone of an electric ball in the electromechanical coupling field was investigated according to variational method,and the corresponding governing equation(Euler-Lagrange equation) was derived.

通过变分原理的方法研究力电耦合场中带电小球的最速降线问题，导出其轨迹控制方程，即Euler-Lagrange方程。

Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory.

为eigenvalues和30个开放式问题也提供古典isoperimetric 不平等的拘谨的赠送，这本书将是对纯并且被使用数学家有用的，特别是对偏微分方程，变分法，不同几何学或者光谱的理论感兴趣的那些。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。