具指数型反应项的半线性抛物型方程组解的爆破速率估计  

Blow-up estimates for semilinear parabolic systems with exponent reaction terms

作　　者：李慧玲[1] 

机构地区：[1]东南大学数学系,南京210096

出　　处：《东南大学学报（自然科学版）》2009年第6期1287-1291,共5页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10701024;10601011);江苏省高校自然科学基金资助项目(09KJD110008)

摘　　要：考虑一类带有齐次Neumann边界条件且反应项为指数形式的半线性抛物型方程组,考察指数型的反应项对解的爆破速率的影响.首先借助于比较原理建立了解的2个分量间的联系,然后运用微积分学的基本技巧和最大值原理,并经一系列计算与估计,得到了爆破解的爆破速率估计.分析发现,对于带有Neumann边界条件的初边值问题,所导出的爆破速率的阶是将该非线性项从方程的右端移至边界条件的右端时所对应的问题的解的爆破速率的阶的2倍.该结果再一次说明,即使对于同一个非线性反应项,如果其处于不同的位置,那么对应问题的爆破解的爆破性质也将发生较大的改变.A semilinear parabolic system with exponent reaction terms and null Neumann boundary conditions is concerned in this paper,mainly about the effect of the exponent reaction terms on blow-up rate estimates.Firstly,a relation between the two components of solutions is established by the comparison principle;secondly,by making use of the maximum principle and series of careful calculations and estimates,blow-up rate estimates are given.For the initial-boundary problems coupled with Neumann boundary conditions,as is known by us,the order of the blow-up rate obtained by the present paper is exactly twice that of the problem,in which such reaction terms are placed at the right-hand sides of the boundary conditions.The result of the present paper illustrates again that even for the same reaction terms,if they appear in different places,the blow-up solutions of the corresponding two problems would possess very different properties.

关 键 词：半线性抛物型方程组 有限时刻爆破 爆破速率估计 

分 类 号：O175.26[理学—数学]