查询词典 blow up

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。

In Chapter 3,we get the global existence and blow-up criteria for the solutions.

在第三章中我们得出了解的整体存在和有限时刻Blow-up的判定准则。

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。

First,we consider the lower semicontinuity property fora functional with linear growth in LDΩthe second, in the SBD space,we discussthe lower semicontinuity of an integral functional that the integrand is a Carathéodoryfunction and that satisfies a symmetric quasi-convex assumption, by the compactnesstheorem of the SBD space,blow-up method and Morrey theorem,prove that integral functional is lower semicontinuous with respect to L~1- convergence;then by using theone-dimentional sections method and the structure theorem of the BD functions, dis-cuss the lower semicontinuity of the integral functional in the whole BD space.

首先我们考虑LD空间满足线性增长的积分泛函的下半连续性；其次在SBD函数空间讨论了被积函数为Carathéodory函数时的积分泛函在满足对称拟凸条件时的下半连续性，主要利用SBD函数空间的紧性定理和blow-up方法以及Morrey定理等给出了积分泛函关于L~1-强收敛的下半连续性；然后利用BD函数的一维截断方法和结构定理，讨论了在BD全空间上的积分泛函的下半连续性。

Based on the maximum principle,we construct the blowing-up lower solution by the relations of parameters and solution of the ordinary differential equation and then the blow-up properties are studied.We use the maximal principle to analyse the derivative profiles of the solution and get the lower bounds and upper bounds of blow-up rate through the complicated analysis technology and the inequality theory.

基于最大值原理的比较理论，通过一些特定的参数关系，利用相关常微分方程的解构造合适的爆破形式的下解，由此得到退化反应系统初边值问题的爆破解；然后，对爆破解的性质进行进一步的研究，利用极大值原理对解的导数特性进行了分析，给出了解的爆破速率的上、下界估计。

When a discussion is made on the blow-up problem for a semilinear development equation with singular cofficient,the solution is usually estimated,then the conditions for the blow-up problem are presented.

讨论奇异半线性发展方程组解的B low-up问题时，通常先对解进行估计，然后讨论在一定条件下解的B low-up。论文继续用这种方法讨论奇异半线性发展方程组解的B low-up问题，得到一定条件下解会B low-up

This is substantially different from the scalar equations with absorptions,whose blow-up rates are all known as absorption-independent.

由于具有吸收的单个方程的奇性解的blow-up速率全都与吸收无关，故与吸收有关的blow-up速率将是具吸收的耦合组问题的特有现象，而本质区别于单个方程问题。

Three possible simultaneous blow-up rates under different dominations of nonlinearities are established.

我们得到了不同非线性指标占优情形下三种可能的blow-up速率。

It is interesting to observe that not only the simultaneous blow-up rates of the components u and v are asymmetric, but also the blow-up rates of the same component u may be in different levels under different dominations.

我们发现一个有趣的现象：这里不仅u和v的速率是不同量级的，而且同一个分量u在不同参数区域的blow-up速率也可能具有不同的量级。

In the first part we consider the case of balanced absorptions,and obtain four absorption-independent simultaneous blow-up rates under different dominations of nonlinearities.

第四章讨论具内吸收的多重耦合热方程组解的有限时刻blow-up问题。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。