查询词典 parabolic partial differential equation

AbstractPaper introduces the exponential function and homogeneous balance method for solving nonlinear partial differential of the exact solution, and then comparing the reference solution, and ultimately new exact traveling wave solution.

摘要论文主要介绍指数函数法和齐次平衡法求解非线性偏微分的精确解，然后对比参考文献的解，最终得到新的精确行波解。

A new hyperbolic function s method for finding exact solutions of nonlinear partial differential equations;2. The control strategy based on hyperbolic function is proposed and relative mathematical model is built.

为此讨论了车辆变速行为的一般规律，提出基于双曲函数的车辆变速控制策略，建立了相应的数学模型，并针对实例进行了具体分析。

Using the characteristic line theory of hyperbolic partial differential equations,relations between the reflected signals and the dielectric parameters of the stratified media are analyzed.

提要 本文根据双曲型偏微分方程的特征线理论分析了分层媒质参数与时域反射信号的因果关系，研究了基于时域反射数据的分层媒质的参数反演的离散化模型。

The underlying method is based on the simple wave solutions of a system of hyperbolic partial differential equations.

基本的方法是以双曲型偏微分方程组的简单波解为根据的。

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

We study the linear hyperbolic partial differential equations.

本论文主要研究线性的双曲型偏微分方程。

"In mathematical analysis, an integral transform useful in solving certain types of partial differential equations."

数学分析中的一种积分变换，可用来解决特定类型的偏微分方程式。

Inverse M-matrices often occur in relation to systems of linear or non-linear equations or eigenvalues problems in a wide variety of areas including finite difference methods for partial differential equations, input-output production and growth model in economics, iterative methods in numerical analysis, and Markov processes in probability and statistics.

其中包括偏微分方程的有限差分法、经济中的投入产出和增长模型、数值分析中的迭代法以及概率论和数理统计中的马尔可夫过程。

The second part(Chapter 4,Chapter 5 and Chapter 6)is devoted to freeboundary problems(inverse boundary value problems or geometric inverse prob-lems)for elliptic systems of partial differential equations in continuum mechanics.

第二部分(即第四章、第五章、第六章)讨论力学中椭圆型方程组的自由边界问题(也称逆边值问题或几何反问题)及数值分析，主要涉及到渗流与气体动力学中的一些问题。

According to invalidate transform between non-linear constraining function and linear constraining function, and the disable partial differential coefficient of first order for objective function, GA has been chosen for the built mathematic mode, also, the conception of GA, its computing process, features, and operating parameters are introduced irrespectively in this article, meantime, a managerial software for oil pipeline's optimization is programmed.

根据优化模型中的非线性约束函数无法化为线性约束函数，目标函数无法求一阶偏导数的特点，本文从众多优化方法中选择遗传算法对所建立的数学模型进行求解，并对遗传算法的概念、计算步骤、特点、运行参数等逐一进行介绍，并编写了输油管道优化运行管理的软件。

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。