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Renormalized solutions of a class of strongly degenerate quasilinear parabolic equation s

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This paper gives the probabilistic interpretation for one system of the second order quasilinear parabolic partial differential equations combined with an algebra equation using fully coupled forward-backward stochastic differential equation.

本文利用完全耦合的正倒向随机微分方程，对一类耦合了一个代数方程的二阶拟线性抛物型偏微分方程系统，给出概率表示。

The theory of parabolic equation was presented,and was applied to the scattering analysis of two dimensional perfectly electric conducting objects.

对抛物线方程算法的基本原理进行了详细论述，并将其运用到二维导体目标的电磁散射特性分析中。

In this thesis, we consider positive solutions of a degenerate parabolic system with homogeneous Dirichlet boundary condition. It is proved that all positive solutions exist globally iff 12≥abλ, whereλ1 is the first eigenvalue of ??

该论文研究一类具有齐次Dirichlet边界条件的退化抛物方程组正解的性质，证明了所有正解整体存在的充要条件是12≥abλ，其中λ1是具有齐次Dirichlet边界条件的？？

A scalable parallel algorithm of block tridiagonal systems for solving the initial boundary value problem of 3D-parabolic equation with the Dirichlet boundary condition is discussed.

对三维抛物型方程带Dirichlet边界条件初边值问题的离散系统使用块三对角可扩展并行算法求解。

In this paper we mainly utilize super and sub solution techniques, use comparision principle and construct appropriate supersolution and subsolution by eigenfunctions to discuss two kinds of nonlocal nolinear parabolic systems with homogeneous Dirichlet boundary condition.

两类非线性抛物方程解的整体存在与爆破性质本文主要利用上下解方法，运用比较原理，通过特征函数等构造适当的上下解讨论了两类抛物型方程组解的整体存在与爆破。

In part two, this thesis is dealt with properties of solutions to a degenerate parabolic system coupled via non-local sources, subject to homogeneous Dirichlet conditions and nonnegative initial data.

第二部分，讨论了一类具有齐次Dirichlet边界条件和非负初值的非局部源耦合的退化抛物系统的第一初边值问题。

The main problem studied in this thesis are properties of positive solutions to a semi-linear parabolic system with non-local nonlinear sources and null Dirichlet boundary conditions.

中文摘要：本论文主要研究了具有非局部源的半线性抛物系统并附加Dirichlet零边值的解的性质，得到了系统古典解的渐近性分析：blow-up速率、blow-up集、边界层估计等问题。

The main problem studied in this thesis are properties of positive solutions to a semi-linear parabolic system with non-local nonlinear sources and null Dirichlet boundary conditions. We give the analysis about asymptotic property: blow-up rate, blow-up set and blow-up profiles.

本论文主要研究了具有非局部源的半线性抛物系统并附加Dirichlet零边值的解的性质，得到了系统古典解的渐近性分析：blow-up速率、blow-up集，边界层估计等问题。

Apparently, the approximate controllability doesn"t hold for generally linear parabolic equations with bounded control. It doesn"t hold for the semilinear heat equations presented there,either. Then, it is proved by analyzing its" solutions that no matter how long the time T is , there are targets that can"t be approximated by the solution of heat equation with Dirichlet boundary conditions;If a given target satisying certain conditions can be reached by the solution of heat equation .

本文先针对两个具体的半线性热方程系统证明了控制加约束后系统是不能控的；然后通过分析方程的解，对带位势及Dirichlet边界条件的热方程系统，无论时间多大，都存在不能控的目标；文中还证明了满足一定条件的目标可达。

Consumer preference ; fuzzy partial ordering relation ; condorect function

消费者偏好；模糊偏序关系； condorect函数

And she doesn't have a cat, she has a Mexican hairless.

而且她不养猫，她养了一只墨西哥无毛犬。