弱解

The basic technique used in this paper is the fixed point theory for dif-ferential equations in Banach space.

我们也找出弱解存在的最大时间范围，并探讨此解在趋近边界时的行为；此外，我们也证明了解对初值条件的连续性。

We prove the L~1-stability of weak solutions for arbitrarily large data on multi-dimensional bounded or periodic domain or whole space.

作为研究的出发点，在第三章里，我们首先考虑弱解的L~1稳定性，通过得到关于密度梯度的新熵估计和精细的能量估计，我们可以证明逼近解的收敛性。

We are interested in the complicated interactions among multi-nonlinearities from double degeneracy and source and flux.

本文所考虑的双重退化模型一般不具有古典解，而只能从弱解及相应的比较原理出发。

Inhomogeneous hyperbolic conservation law; viscosity solution; weak solution; entropy-entropy flux; maximum principle; Young measure; Dirac measure; compensated compectness

基础科学，数学，数学分析非齐次双曲型守恒律；粘性解；弱解；熵-熵通量；极值原理； Young测度； Dirac测度；补偿列紧理论

Second, based on the proposed weak formulation, we investigate the numerical solutionsof the time fractional diffusion equation.

基于上述弱解理论，我们计算时间分数阶扩散方程的数值解。

It is therefore essential to devise some kind of proper notion of generalized or weak solution.

所以，设计一个合适的广义解或弱解的适当的定义，这是非常重要的，但是一个巧妙的任务。

If the weak solution can be proved to be unique, it is called the generalized solution.

若能证明弱解是唯一的，则称之为广义解。

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 current st...

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。

Through studing the weak solution in Sobolev space,its solvability has been proved.

通过在Sobolev 空间中对弱解的讨论，证明了它的可解性。

The existence of the solution we have defined is proved by regularized method and weakly convergent technique.

我们所定义的弱解的存在性是通过正则化方法以及弱收敛技巧得到的。

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。