1) blow-up set
爆破点集
1.
Firstly,we construct a comparision theorem,then we prove the existence and uniqueness results of local solution and the solution will blow-up at a finite time when the initial data are large enough by using upper and lower solution method,lastly,we prove the blow-up set is the whole interval .
最后,还证明了爆破点集就是整个区间[0,a]。
2.
Moreover, we show that the blow-up set is the entire interval [0,a].
该文研究双退化的半线性抛物型方程:xrut-xαuxx=∫a0f(u)dx初边值问题,证明了局部解的存在唯一性并且得到当初值充分大时解在有限时刻爆破,得到了解的爆破点集是整个区间[0,a]。
2) blow-up set
爆破集
1.
The blow-up set of the positive solutions of a class of quasilinear parabolic equations subject to Dirichlet boundary conditions was studied,which deepened ones from the corresponding work of Friedman in 1987.
主要研究了一般拟线性抛物型方程在Dirichlet边界条件下正解的爆破集,是Friedman 1987年结果的重要推进。
2.
By the maximum principles and reflection principles,the blow-up of positive solutions of a biomathematics model was studied,and blow-up set and blow-up rate are obtained.
利用反演原理和极值原理讨论了一类生物数学模型正解的爆破现象,获得了解的爆破集和爆破率。
3.
The blow-up rate is determined with the blow-up set,and the blow-up profile near the blow-up time is obtained.
研究了一类带有内部吸收项以及边界条件为指数形式的反应扩散方程解的性质,得到了爆破集,爆破率以及临近爆破时间的爆破行为。
3) explodable set
爆破集
1.
In relation to explodable set of quasiconformal mapping, the author studies its properties; and finds a sufficient condition for judging hyperbolic area of a set on a plane to be infinite; and estimates hyperbolic area of radial K quasiconformal mapping; and improves corresponding results obtained recently by Porter and Reséndis.
研究平面拟共形映照的爆破集性质 。
4) Blow-up point
爆破点
1.
The necessary and sufficient conditions for the solution to have a finite time blow-up, theexact blow-up rates and localization of blow-up points are given.
本文考虑一类半线性热方程组的解，给出了解爆破的充分必要条件，爆破速率和爆破点的位置。
2.
By techniques such as the energy equation, differential inequation and integral inequation, the instability and the blow-up point of the solution are obtained and the L2-concentration of the blow-up solution is established.
本文在n维空间中讨论一类带调和势的非线性Klein-Gordon方程的初值问题,在得到其局部解存在性的基础之上,应用能量方法和微分、积分不等式技巧,得到了在一定条件下解的爆破性质,并进一步讨论了解的爆破点与L2-集中性质。
6) Node blasting
节点爆破
补充资料：点集拓扑
点集拓扑学（point set topology），有时也被称为一般拓扑学（general topology），是数学的拓扑学的一个分支。它研究拓扑空间以及定义在其上的数学构造的基本性质。这一分支起源于以下几个领域：对实数轴上点集的细致研究，流形的概念，度量空间的概念，以及早期的泛函分析。它的表述形式大概在1940年左右就已经成文化了。通过这种可以为所有数学分支适用的表述形式，点集拓扑学基本上抓住了所有的对连续性的直观认识。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条