非局部边界抛物型方程组解的整体存在与爆破性质  

Global Existence and Blow-up Properties for a Parabolic System with Nonlocal Boundaries

作　　者：凌征球[1] 王泽佳[2] 杜润梅[3] 

机构地区：[1]玉林师范学院数学与信息科学学院,广西玉林537000 [2]江西师范大学数学与信息科学学院,南昌330022 [3]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2012年第6期1109-1114,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11071100);广西自然科学基金(批准号:2011jjA10044);吉林大学研究生创新基金(批准号:20121031)

摘　　要：研究具有非局部边界和非局部源项的一类抛物型方程组非负解的整体存在与爆破性.用上下解方法得到了方程组解的临界指数p=(p1+q1)…(pk+qk)-1,证明了:当p≤0,且0≤∫Ωψi(x,y)dy<1时,方程组存在整体解;当p>0时,对于充分大的初值,方程组的解在有限时刻爆破.并讨论了解的爆破率.结果表明,初值和指数的大小对方程组的解有较大影响.The authors investigated the global existence and blow-up properties of nonnegative solutions for a class of nonlocal parabolic systems with nonlocal boundary conditions. With the help of the super- and sub-solution methods, the critical exponent of system was gained. And it＇s proved that if p= （P1＋q1）（Pk＋qk）- 140 and 0 whereas if p〉0, then the solution Moveover, the exact rate of the blow and exponents play an important role （x,y）dy 〈 1, every nonnegative solution is global, blows-up in finite time if the initial data is sufficiently large. -up is obtained. The results show that the size of initial values in the properties of the solutions.

关 键 词：抛物系统 整体存在 爆破 爆破率 

分 类 号：O175.2[理学—数学]