非局部的退化抛物型方程组的解的爆破和整体存在性  

Blow-up and Global Existence for a Nonlocal Degenerate Parabolic System

作　　者：陈玉娟[1] 

机构地区：[1]南通大学理学院,南通226007

出　　处：《数学物理学报（A辑）》2006年第5期731-740,共10页Acta Mathematica Scientia

基　　金：江苏省高校自然科学研究计划项目(04KJB110108)资助

摘　　要：该文采用弱上下解方法以及正则化的技巧,研究了一类非局部的退化的抛物型方程组的解的爆破和整体存在性,给出了方程组的解的爆破指标p_c=(p_1+p_2)(q_1+q_2)-mn,证得当p_c＜0时,对任意的初值,方程组的解整体存在；当p_c＞0时,对充分大的初值,解在有限时刻爆破,对充分小的初值,解整体存在；当p_c=0时,若区域充分小,则方程组存在非负整体解,若区域包含了一个充分大的球,则解在有限时刻爆破．This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system. The sub and super solutions method and the regularization skill are used. The critical exponent of the system is gained. It＇s proved that if pc = （P1 ＋ P2）（q1 ＋ q2） -mn 〈 0, every nonnegative solution is global, whereas if pc 〉 0, there exists both global and blow-up nonnegative solution. When pc = 0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain is large enough that is, if it contains a sufficiently large ball, there is no global solution. The related results of papers [8,10,11] are the special cases of this paper.

关 键 词：退化方程组 非局部源 爆破 

分 类 号：O175.26[理学—数学]