弱解

Huang and Lin proposed the weak solution concept for Backward Stochastic Differential Equation This paper based on the predecessor's work , gives the weak solution concept for Backward Stochastic Differential Equation with continuous martingale,uses the Girsanov transformation, obtains its weak solution of the existence of a necessary and sufficient conditions, and on this basis obtains its weak solution of the existence of sufficient conditions,these sufficient conditions weakened the drifting coefficient which requested in the existence uniqueness of strong solution to satisfy the Lipschitz condition the request.

本文在前人研究的基础上，给出由连续鞅驱动的倒向随机微分方程弱解的概念，利用Girsanov变换，得到其弱解存在的存在的一个充分必要条件，并在此基础上得到了其弱解存在的一些充分条件，这些充分条件减弱了在强解的存在唯一性中要求的漂移系数满足Lipschitz条件的要求。

We deal with the biharmonic equation and proved that under our assumptions, the week solution of the natural boundary value problem strongly converges (in H~2) to that of the first boundary value problem.

为克服这一困难，我们用具自然边界条件的边值问题(在二阶椭圆型方程情形为第三边值问题)去逼近相应的第一边值问题，并以重调和方程为例，证明了在一定条件下，其具自然边界条件的边值问题的弱解在H~2的意义下强收敛到相应的第一边值问题的弱解。

In first chapter,we discuss the〓-integrability of thegradients of the very weak solutions to non-linear elliptic systemsdivA=B(2)and〓-regularity of the very weak or the weak solutions to non-linearelliptic systems〓(3)in bounded domain Ω.

第一章讨论有界区域上的非线性椭圆型方程组〓（2）的很弱解的梯度的〓可积性和非线性椭圆型方程组〓（3）的很弱解与弱解的〓正则性。

The asymptotic behavior of the weak solution is obtained when an enthalpy function is made in L(superscript 2 subscript +) and a differential inequality is proved after using Cauchy inequality, Poincare inequality and the definition of weak solution.

在L(上标2 下标+)空间上构造了一个熵函数，利用带ε的Cauchy不等式和poincare不等式及弱解的定义，推导出了此函数满足的一个微分方程不等式，通过求解微分方程，证明了弱解的渐近性问题。

In this thesis, we study Cauchy rational interpolation problem on the set of distinct nodes by algebraic method and give some algorithms in univariate and multivariate cases.

我们推广了有理插值问题解的概念，给出了扩展弱解，弱解和解的定义，并且说明在给定一个代数结构后扩展弱解集构成一个线性空间。

Two conservation equations are derived from a Wigner-Fokker-Planck model, they contain a third-order quantum correction term and second-order viscous term...

然后 在弱的亚音速条件下利用截断技术建立解的先验估计，在此基础上根据Leray-Schauder 不动点定理得到四阶方程弱解的存在性。

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。

Under the Lipschitz conditions,using Morrey space and Campanatospace methods and filling-hole technique to clear off the difficulty,whicharoused by that monotonic inequalities are no longer true and blow-uptechnique are very difficult to be used again,we obtain that the weaksolutions or the very weak solutions to systems(3)are locally Holdercontinuous.

对方程组（3），我们增加了Lipschitz条件，利用Morrey空间法和Campanato空间法和补洞技巧等来克服非齐次项带来的，单调不等式不再成立和Blow-up技巧难于适用的困难，得出了方程组（3）在一定的条件下的很弱解和弱解是局部〓连续的。

The main goal of the thesis is to study such some problems as theexistence of weak solutions of quasilinear elliptic equations involvingcritical Sobolev exponents on a bounded domain and〓,the unique-ness of weak solutions、regularity of weak solutions、stability ofweak solution on exponent p、continuity of very weak solutions ondomains、the fusion problem of weak solutions and the existenceof minimal positive solution of a class of quasilinear elliptic obstacleproblems,which have been extensively concerned,but have not beensolved satisfactorily in the latest several years.

本文主要对近年来人们普遍关注而又没有完全解决的几个问题——有界域及无界域上带临界增长的拟线性椭圆方程弱解的存在性，弱解、很弱解的唯一性、正则性，解关于区域的连续依赖性，解关于指数的稳定性，弱解、很弱解的合并问题，以及椭圆型偏微分方程对应的障碍问题极小正解的存在性等进行研究。

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。