弱解

First, we use the time-descrete method for constructing an approximate solution, hence, establish a priori estimates of the approximate solution,we prove the existence subsequently by taking the limit of the approximate solution.

首先， 我们用时间离散化的办法构造逼近解，再对逼近解作必要的一致估计，然后通过对逼近解取极限，证明了弱解的存在性。

O1 c compactness of the entropy equation; At last, coupling with Kinetic formulation, we can obtain the existence of a strong convergent sequence, then the limit function is just the entropy weak solution of the original systems.3. Existence of global entropy solutions to an inhomogeneous elastodynamics system.

o1 c紧性，最后结合Kinetic理论得到粘性解存在强收敛的子列，从而可得该极限函数即为原方程组的熵弱解。3、研究了一类非齐次弹性力学方程组整体熵解的存在性。

In this paper, we just consider the initial-boundary value problems of aclass of two-dimensional nonlinear integro-differential equation, simultaneouslyconsidering the damped term and memory termThe details will go as follows. Firstly, the c...

本文同时考虑耗散项和记忆项等因素，讨论了一类具有记忆项的二维非线性积分微分方程的如下初边值问题具体研究内容如下：首先，文章简单介绍了国内外当前对非线性积分微分方程的研究现状；其次，文章给出了一些重要概念和引理，并对部分符号做了说明；第三，利用Galerkin方法证明了问题(1)-(3)的变形问题弱解的存在唯一性；第四，证明了问题(1)-(3)强解的存在性和能量的指数衰减性；第五，进一步证明了问题(1)-(3)经典解的存在性。

In this article, the existence and uniqueness of the generalized solution of this boundary value problem are discussed, the existence and convergence of Galerkin's approximate solution is proved, and Linear dependence of the the error bound on M~2/(1-M~2) is also proved, where M is Ma...

本文证明了这类方程弱解的存在和Galerkin逼近解的存在和收敛，并且还给出了有限元解的误差估计，指出误差界线性地依赖于M~2/(1—M~2)。M为马赫数。也就是说，当流速接近音速时，有限元解的误差将无法控制。

The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied. Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained.

研究具非线性边界条件的一类广义Ginzburg＿Landau方程解的整体存在性·推导了Ginzburg＿Landau方程的非齐次初边值问题光滑解的几个积分恒等式，由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计；通过逼近技巧、先验估计和取极限方法证明了Ginzburg＿Landau方程的非齐次初边值问题整体弱解的存在性

First, the paper presents mathematically the existence of a solution in the weak formulation of SBV space.

首先在数学上指出了 MS泛函弱解在 SBV函数空间中的存在性，然后讨论了计算弱解的数值逼近方法。

The energy inequality and parabolic monotonici ty inequality is essential for the regularity of a weak solution to this problem .

该问题弱解的能量不等式和抛物单调不等式在证明弱解的正则性时起关键作用。

In order to understand the weak solutions like piece-wise smooth solution, we must investigate the structures and properties of global smooth solution.

一般情况下，要研究清楚分块光滑解等常见的弱解，我们必须研究光滑解尤其是全局光滑解的结构和性质，这是研究高维守恒律方程方程全局解的基础。但用以往的处理方法一般来说是很困难的。

By studying the known concepts and methods, this paper quotes a new concept of weak solution of the above equation. This concept contains some important information, which had been lost in the old definitions.

基于已有的研究基础上，本文对上述方程提出了一个新的弱解概念，该概念隐含了原来所定义的弱解所丢弃的一些有用的信息。

Under weaker conditions(without theirhomogeneous conditions,monotonic inequalities and Lipschitz conditions)than that which Iwaniec and other people imposed on some specialsystems(quasi-regular mappings),using Hodge decomposition theoremto construct testing function,after a series of complicated calculation,weobtain the same regularity results as them to a more general non-linearelliptic systems(2):under certain conditions,the very weak solutionsto non-linear elliptic systems(2)are weak solutions.

对一般的方程组（2），我们减弱了Iwaniec等的齐次性条件、单调不等式以及Lipschitz型条件，利用Hodge分解定理来构造试验函数，并进行了一系列复杂的计算，在没有Lipschitz型条件的情况下，也得到了与itz型条件的情况下，也得到了与，即在一定的条件下，方程组（2）的很弱解是弱解。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。