守恒律

A L∞bound estimate is provided on the solutions of a semi-linear parabolic system by the theory of phase transitions.The existence of solutions of corresponding hyperbolic system of conservation laws is studied by viscosity methods and compensated compactness framework.

讨论来源于物理相变理论的一类半线性抛物型方程组解的一致L∞估计，该结果是利用粘性法和补偿列紧框架研究相应的双曲型守恒律解的存在性的重要内容。

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。

The research on numerical method for hyperbolic conservation laws is one of the important directions in computational mathematics.

中文摘要：双曲型守恒律方程数值方法的研究，是计算数学中的一个重要研究方向。

And many finite difference schemes have been widely used to solve hyperbolic conservation laws.

有限差分格式已经被广泛应用于守恒律方程的求解。

The key problem of the reaction chromatography is the initial-boundary value problem for hyperbolic conservation laws systems.

反应色谱的核心问题是双曲守恒律的初边值问题。

Under the prerequisite that the field variables exist with any reasonable boundary conditions, the infinitesimal symmetrical transformation is obtained.

在场变量可为任意合理解的前题下，确定了无穷小对称变换，并发现不变性条件包含了物理空间和物质空间中的守恒律。

PartⅡis devoted to studying integrability of nonlinear DDEs from the view of conservation law starting from scaling symmetry.

第二部分研究非线性DDE守恒律的待定系数构造算法。

Secondly, by introducing the generators of the infinitesimal transformations of Jourdain, the Noether′s theorem for the above nonholonomic systems of variable mass in event space has been obtained, which is based upon the invariance of the differential variational principle under the infinitesimal transformations of group.

这一成果揭示了力学系统的守恒量和其内在的对称性的关系，极大地推动了力学、物理学的发展。在近20年来，国内外的许多学者相继对Noether定理做了多方面的推广，不但用Hamilton作用量而且用微分变分原理研究完整和非完整系统的守恒律。

As long as the system of first order polynomial DDEs in (1+1)-dimensions is given, no matter whether a single equation or the coupled equation, CLawDDEs can automatically output the scaling symmetries of the variables and a series of possible polynomial conservation laws for different rank.

只要输入多项式形式的等秩DDE，无论是单个方程还是耦合方程组，CLawDDEs都能自动确定变量的标度变换特性和不同秩的多项式守恒律。

The model consists of the conservation laws for the electron density and the current density coupled to the Poisson equation for the electrostatic potential.

该模型由电子密度和电流密度的守恒律方程组相合上关于静电位势的Poisson方程而组成。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。