| 非局部边界抛物型方程组解的整体存在与爆破性质 |
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| 引用本文： | 凌征球,王泽佳,杜润梅.非局部边界抛物型方程组解的整体存在与爆破性质[J].吉林大学学报(理学版),2012,50(6):1109-1114. |
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| 作者姓名： | 凌征球 王泽佳 杜润梅 |
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| 作者单位： | 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 |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | 抛物系统 整体存在 爆破 爆破率 |
| 收稿时间： | 2012-03-14 |
Global Existence and Blow-up Properties for a Parabolic System with Nonlocal Boundaries |
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| LING Zheng-qiu,WANG Ze-jia,DU Run-mei.Global Existence and Blow-up Properties for a Parabolic System with Nonlocal Boundaries[J].Journal of Jilin University: Sci Ed,2012,50(6):1109-1114. |
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| Authors: | LING Zheng-qiu WANG Ze-jia DU Run-mei |
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| Institution: | 1. Institute of Mathematics and Information Science, Yulin Normal University, Yulin 537000,Guangxi Zhuang Autonomous Region, China|2. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;3. Institute of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | 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)-1,p≤0 and 0≤∫Ωψi(x,y)dy<1, every nonnegative solution is global, whereas if p>0, then the solution blows\|up in finite time if the initial data is sufficiently large. Moveover, the exact rate of the blow\|up is obtained. The results show that the size of initial values and exponents play an important role in the properties of the solutions. |
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| Keywords: | parabolic system global existence blow up blow up rate |
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