一类对数形式退缩抛物型方程组解的整体存在性与爆破  

Global Existence and Blow-up for a Degenerate Parabolic System Come from Logarithmic Function

作　　者：孙仁斌[1] Sun Renbin(College of Mathematics and Statistics, South-Central University for Nationalities , Wuhan 430074 , Chin)

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2017年第1期119-122,共4页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(61374085)

摘　　要：考虑了一类由对数函数产生的退缩抛物型方程组的初边值问题,利用逼近的方法得到了解的局部存在性.通过特征函数构造的上解得到了解整体存在的条件,利用特征函数得到了解在有限时刻爆破的条件及爆破时间的上限.In this paper,a class of initial-boundary value problem of degenerate parabolic system come from logarithmic function was considered. The local existence of solution was proved by approximation method. The condition of global existence of the solution was obtained by the upper solution of the characteristic function,and the blow-up condition and the upper bound of the blow-up time were obtained by using the characteristic function.

关 键 词：退缩抛物型方程组 局部解 整体解 爆破 

分 类 号：O175.26[理学—数学]