And just to tell you again that is a strange partial differential equation relating these two vector fields.
再说明一下，这是关于这两个向量场，多少有点奇怪的偏微分方程。
So the unknown is a function, and the equation will relate the partial derivatives of that function to each other.
未知量是一个函数，这个方程，将把函数的偏导数联系起来。
Basically, to every problem you might want to consider there is a partial differential equation to solve.
总的来讲，所有你想解决的问题，都可以用偏微分方程来做。
Partial differential equation is widely used in problems of science and engineering.
偏微分方程在科学和工程上有着广泛的应用。
But this partial differential equation can not be directly integral, so usually use Navier method, Rayleigh Ritz method and finite difference method and other methods.
但这一偏微分方程不能直接积分，所以通常用纳维法、瑞利-里兹法、有限差分方法等方法求解。
The mixed partial differential terms of time variables and space variables in the pseudo-parabolic equation make the discussion of the difference scheme more difficult.
伪抛物型方程中关于时间与空间变量的混合偏导项给差分格式的讨论带来了一定难度。
A nonlinear partial differential equation model based on nonlocal information was proposed to remove noise and preserve the edges.
针对传统扩散模型中的边界模糊问题，提出一种基于非局部信息的非线性偏微分方程去噪模型。
It is a new method to generate surfaces with partial differential equation (PDE).
用偏微分方程(PDE)构造曲面是一种新兴的曲面造型方法。
In recent years, many partial differential equation problems are also appeared in life science and economics.
近年来，在生命科学、经济学中也出现了大量的偏微分方程问题。
Furthermore, the author gives the oscillation criteria of some partial difference equation with continuous variables.
此外，作者还给出了一类具有连续变量的偏差分方程的振动准则。
It is very difficult to get analytic solution except some very specific cases for the model owing to nonlinear partial differential equation.
由于非饱和流动的数学模型归结为非线性的偏微分方程，除了一些很特殊的情况外，很难得到解析解。
In this paper, we get a method to solve a non-linear RH problem by the Cauchy-Riemann conditions and the theories of partial differential equation.
利用柯西黎曼条件和偏微分方程理论，得到了一类非线性RH问题的求解方法，并通过实例表明该方法是可行的。
A high accuracy algorithm for numerical solution of nonlinear partial differential equation (PDE) is suggested combining wavelet collocation method with generalized energy integral.
将小波配置法与广义能量积分相结合，提出了一种求解非线性偏微分方程的高精度数值方法。
For example, the temperature of a metal plate can be expressed as a partial differential equation if the temperature on the boundaries is known. This is called a boundary value problem.
比方说，如果已知一块金属板边界上的温度，那么整块金属板的温度就可由一个偏微分方程表示，这称为边值问题。
The partial differential equation of flow in porous medium has been studied with variational finite element method.
用变分有限元方法对描述地下流体渗流的偏微分方程进行了分析。
Consider the distributed parameter system described by the second order partial differential equation of composed type, we discuss its a boundary optimal control problem with quadratic performance.
考虑用二阶复合型偏微分方程所描述的分布参数系统，研究了它的一个使平方性能指标达到最小值的边界最优控制问题。
This paper proposes a new method of solving the high order linear partial differential equation by means of Walsh Series.
本文提出了用沃尔什级数求解高阶线性偏微分方程的一种新方法。
An effective method for solving a partial differential equation of secondary hydrocarbon migration is put forward.
本文给出了一种高效率求解油气二次运移偏微分方程的方法。
The partial differential equation is solved by Alternating Direction Implicit algorithm.
采用交替方向隐式算法求解偏微分方程。
A condition of a one-order quasilinear partial differential equation of a traffic model forming unique shock wave is given end proved.
本文讨论了一交通模型的一阶拟线性偏微分方程激波产生唯一性的条件并给了严格的证明。
According to the diffusibility of the photons transmission, numerical solution of photon transmission partial differential equation was deduced with finite element.
依据光子传输的扩散性，用有限元法导出光子传输扩散偏微分方程的数值解。
The mathematical physical model is established depending on the conventional laser heat treatment technology, the partial differential equation of heat current propagation is derived.
本文以常规的激光热处理工艺为基础，建立相应的数学物理模型，导出热流传导的偏微分方程。
According to the assumption of slightly compressible fluid, neglected the quadratic gradient term in nonlinear partial differential equation is usually lead to error.
在非线性偏微分方程中，根据弱可压缩液体的假设，忽略二次梯度项，在试井较长时间内将产生误差。
Axisymmetric elasticity problem of cubic quasicrystal is reduced to a solution of a partial differential equation with higher-order by introducing displacement function.
本文通过引入位移函数使得立方准晶的轴对称弹性问题化为求解一高阶偏微分方程。
In this paper, we study the pricing problem of the perpetual Bermudan option with jump-diffusion by PDE (partial differential equation) method.
采用偏微分方程方法讨论了带跳扩散项的永久百慕大期权定价问题。
First, the neutron diffusion equation is converted to three coupled one dimensional partial flux equation through transverse integration.
首先通过横向积分将中子扩散方程化为三个互相耦合的一维偏通量方程。
In this paper we constructed an exponentially fitted difference scheme for singular perturbation problem of hyperbolic-parabolic partial differential equation.
本文对双曲-抛物偏微分方程奇异摄动问题构造了一个指数型拟合差分格式。
In physics, the physical parameter evolution along with the time is often controlled by the non-linear partial differential equation.
在物理学中，物理参量随时间的演化往往是由非线性的偏微分方程支配的。
The algorithm for a class of optimal control problem where the state variables are the weak solution of an elliptic partial differential equation is studied.
研究一类最优控制问题的求解方法，其状态变量是某一种椭圆型偏微分方程的弱解。
The algorithm for a class of optimal control problem where the state variables are the weak solution of an elliptic partial differential equation is studied.
研究一类最优控制问题的求解方法，其状态变量是某一种椭圆型偏微分方程的弱解。
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