具有对数奇性耦合的半线性抛物方程组的全局解与猝灭  

On Global Existence and Quenching in a Coupled Logarithmic Singular Semilinear Parabolic System

作　　者：孙仁斌[1] 袁海峰[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）》2012年第2期113-116,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(10771219)

摘　　要：研究了具有对数奇性耦合的半线性抛物方程组的初边值问题,利用上、下解法和特征函数法,得到了当区域的直径小于某个常数时解是全局存在的,当区域的直径适当大时,解会在有限时刻发生猝灭,并给出了猝灭时刻的上、下界的估计.In this paper, a kind of initial-boundary-value problems for semilinear parabolic system with logarithmic singular coupling is studied. By the method of upper and lower solution and the method of eigenfunction, it is proved that the solutions of the problem are global for adequate small region such that the diameter of the region less than certain constant while the solutions quench in finite time for adequate large region. The upper and lower bound of quenching time is estimated.

关 键 词：对数奇异项 抛物方程组 整体解 有限猝灭 猝灭时间 

分 类 号：O175.26[理学—数学]