查询词典 evolution equation

Studies show that the acoustic wave equation can be derived from Its evolution equation at the macroscopic limit.

研究表明，这样一种离散粒子系统中的统计平均量随时间的变化具有波动规律。

In chapter 3, homogeneous balance method is used to deal with some problems of finding solutions of higher dimensional nonlinear evolution equation . By improving some key procedure of the method, the original equation is reduced to a linear equation , hence a great number of exact solutions for this are obtained.

第三章利用齐次平衡法研究了一些高维非线性演化方程和方程组的求解问题，通过对该方法的某些关键步骤的处理，将原方程转化为一线性的微分方程，从而获得了这些方程大量的多种精确解。

Indeed, it is not clear whether one should interpret the Dirac equation as a quantum mechanical evolution equation, like the Schrodinger equation for single particle.

事实上，人们是否应该将Dirac方程解释为量子力学的进展方程也不是清楚的，像单粒子的Schrodinge方程那样。

From this equation we obtain the evolution equation of the image surface using the connection of the surface evolution and its level lines.

由这个演化方程，利用曲面演化和其水平线演化之间的关系，得到关于图像曲面的演化方程。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

The nonexistence of global weak solution to elliptic equation and the evolution equation, together with the nonexistence of local weak solution to hyperbolic equation is contained in this paper.

本文运用试验函数法研究了带有非局部源的偏微分方程的全局弱解的不存在性，内容包括椭圆方程、发展方程全局解的不存在性以及双曲型方程的局部弱解的不存在性。

In this thesis,we mainly study the following three type of equations under certain non-Lipschitz conditions: stochastic Volterra type integral equation,backward stochastic Volterra type integral equation(including two cases:with jump and in infinite dimensional space),multivalued stochastic evolution equation.

本文将在某些给定的非Lipschitz条件下，依次讨论随机Volterra型积分方程，倒向随机Volterra型积分方程(包括带跳情况和无穷维情况)，多值随机发展方程。

Based on Chaboche's Continuum Damage Mechanics Model, this study suggested low-cycle fatigue damage model under nonproportional loading, in which maximum shear stress and mean hydrostatic stress are considered as two basic parameters and nonproportionality of loading path is considered as a damage parameter to enter damage evolution equation which may well describe damage evolution law of low-cycle fatigue under nonproportional loading.

按Chaboche的连续损伤力学方法建立的多轴非比例加载下低周疲劳损伤模型，以最大剪应力和平均静水应力作为两个基本参量，将路径的非比例度作为损伤参量引入损伤演化方程中，可以较好地描述非比例加载下低周疲劳的损伤演化。

In this paper, we study nonlinear perturbation analysis of mesoscale verticalcirculation and evolution equation by means of f plane, non-hydrostatic balance andfilter model. Outstanding nonlinear characteristic of mesoscale disturbance invertical direction, we obtain nonlinear symmetric disturbance equation anddisturbance amplitude s evolution equation by use of multi-scale and singularperturbation technique.

中文摘要：本文采用f平面、非静力平衡、滤声波模式，讨论了大气中尺度非线性动力学方程，通过尺度分析重点突出了扰动在垂直方向上的非线性特征，从而得到了对称扰动非线性方程，运用多重尺度方法和摄动分析讨论了对称扰动非线性重力惯性波的演化过程，得到非线性重力惯性波振幅演化服从广义的非线性Schrdinger方程。

Based on Stuart et al.'s electron density evolution equation, the electron density evolution process in fused silica film irradiated by short-pulse laser for τ∈[0.015] ps were studied by means of numerical method. The effects of initial electron density N and laser pulse width τ on laser threshold intensity I and damage threshold fluence. F were analyzed respectively.

基于STUART等人的电子密度演化方程，运用数值模拟方法，研究了脉宽为τ∈[0.01， 5]ps范围内单脉冲激光作用下熔融石英薄膜中电子密度演化过程；讨论了初始电子密度、激光脉冲宽度对阈值功率密度和阈值能量的影响；分析了初始电子密度、激光脉冲宽度对多光子离化及雪崩离化的影响。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。