半线性抛物型方程解在有限时刻猝灭与解整体存在的条件  

Conditions on Quenching in Finite Time and Global Existence for Semi-Linear Parabolic Equation

作　　者：孙仁斌[1] 

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）》2014年第1期118-122,共5页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家民委科研基金资助项目(12ZNZ004)

摘　　要：考虑一类含有奇性反应函数的半线性抛物型方程的初边值问题,首先讨论了解在有限时刻发生猝灭的条件与在猝灭时刻解对时间导数的爆破性,得到了猝灭时刻的上限估计,而后在球形区域内讨论了整体解存在的条件.In this paper , we consider a class of initial-boundary value problem of semi-linear parabolic differential equation with singular term.Firstly, we prove that the solution quenches and the derivate of solution to time blows up in some finite time, get the estimation value for the upper limit of quenching time , and then discuss existence condition of the global solution in a ball .

关 键 词：抛物型方程 猝灭 爆破 整体解 

分 类 号：O175.26[理学—数学]