具有非局部源项的抛物型方程组正解的爆破与爆破率  

Blow-up and Blow-up Rate for a Nonlocal Parabolic System

作　　者：凌征球[1] 龚文振[1] 

机构地区：[1]玉林师范学院数学与信息科学学院,玉林537000

出　　处：《工程数学学报》2014年第1期84-92,共9页Chinese Journal of Engineering Mathematics

基　　金：广西自然科学基金(2010GXNSFA013125)~~

摘　　要：本文研究一类具有齐次Dirichlet边界条件与非局部源项耦合的半线性抛物型方程组的初边值问题.该问题来源于可燃混合气体的热传播过程等自然现象.利用椭圆问题的特征值与特征函数理论和上解下解方法,我们给出了该问题解的临界指标p=p1p2···pk-1.征得当p≤0,且pi>qi,以及系数ri充分小时,问题存在整体解.而如果p>0,则对于充分大的初值,我们证得解在有限时刻爆破.另外,我们证明获得了爆破率的上界.The initial-boundary value problem of the semilinear parabolic system coupled via nonlocal sources, subjecting to the homogeneous Dirichlet boundary condition, is investigated in this paper. The problem is derived from the natural phenomena such as heat propagation of the combustible mixture gases. The critical exponent p=p1p2 ···pk-1 of this problem is gained by means of the eigenvalue and eigenfunction theory and the methods of supersolution and subsolution. It is proved that under the condition that p ≤ 0, pi 〉 qi, and ri is small enough, every solution to the problem is global, whereas if p 〉 0 and the initial data are sufficiently large, then the solution blows up in a finite time. In addition, the upper bound of the blow-up rate is also obtained.

关 键 词：抛物系统 整体存在性 爆破 爆破率 

分 类 号：O175.2[理学—数学]